# torch_geometric.utils

 scatter Reduces all values from the src tensor at the indices specified in the index tensor along a given dimension dim. group_argsort Returns the indices that sort the tensor src along a given dimension in ascending order by value. segment Reduces all values in the first dimension of the src tensor within the ranges specified in the ptr. index_sort Sorts the elements of the inputs tensor in ascending order. cumsum Returns the cumulative sum of elements of x. degree Computes the (unweighted) degree of a given one-dimensional index tensor. softmax Computes a sparsely evaluated softmax. lexsort Performs an indirect stable sort using a sequence of keys. sort_edge_index Row-wise sorts edge_index. coalesce Row-wise sorts edge_index and removes its duplicated entries. is_undirected Returns True if the graph given by edge_index is undirected. to_undirected Converts the graph given by edge_index to an undirected graph such that $$(j,i) \in \mathcal{E}$$ for every edge $$(i,j) \in \mathcal{E}$$. contains_self_loops Returns True if the graph given by edge_index contains self-loops. remove_self_loops Removes every self-loop in the graph given by edge_index, so that $$(i,i) \not\in \mathcal{E}$$ for every $$i \in \mathcal{V}$$. segregate_self_loops Segregates self-loops from the graph. add_self_loops Adds a self-loop $$(i,i) \in \mathcal{E}$$ to every node $$i \in \mathcal{V}$$ in the graph given by edge_index. add_remaining_self_loops Adds remaining self-loop $$(i,i) \in \mathcal{E}$$ to every node $$i \in \mathcal{V}$$ in the graph given by edge_index. get_self_loop_attr Returns the edge features or weights of self-loops $$(i, i)$$ of every node $$i \in \mathcal{V}$$ in the graph given by edge_index. contains_isolated_nodes Returns True if the graph given by edge_index contains isolated nodes. remove_isolated_nodes Removes the isolated nodes from the graph given by edge_index with optional edge attributes edge_attr. get_num_hops Returns the number of hops the model is aggregating information from. subgraph Returns the induced subgraph of (edge_index, edge_attr) containing the nodes in subset. bipartite_subgraph Returns the induced subgraph of the bipartite graph (edge_index, edge_attr) containing the nodes in subset. k_hop_subgraph Computes the induced subgraph of edge_index around all nodes in node_idx reachable within $$k$$ hops. dropout_node Randomly drops nodes from the adjacency matrix edge_index with probability p using samples from a Bernoulli distribution. dropout_edge Randomly drops edges from the adjacency matrix edge_index with probability p using samples from a Bernoulli distribution. dropout_path Drops edges from the adjacency matrix edge_index based on random walks. dropout_adj Randomly drops edges from the adjacency matrix (edge_index, edge_attr) with probability p using samples from a Bernoulli distribution. homophily The homophily of a graph characterizes how likely nodes with the same label are near each other in a graph. assortativity The degree assortativity coefficient from the "Mixing patterns in networks" paper. get_laplacian Computes the graph Laplacian of the graph given by edge_index and optional edge_weight. get_mesh_laplacian Computes the mesh Laplacian of a mesh given by pos and face. mask_select Returns a new tensor which masks the src tensor along the dimension dim according to the boolean mask mask. index_to_mask Converts indices to a mask representation. mask_to_index Converts a mask to an index representation. select Selects the input tensor or input list according to a given index or mask vector. narrow Narrows the input tensor or input list to the specified range. to_dense_batch Given a sparse batch of node features $$\mathbf{X} \in \mathbb{R}^{(N_1 + \ldots + N_B) \times F}$$ (with $$N_i$$ indicating the number of nodes in graph $$i$$), creates a dense node feature tensor $$\mathbf{X} \in \mathbb{R}^{B \times N_{\max} \times F}$$ (with $$N_{\max} = \max_i^B N_i$$). to_dense_adj Converts batched sparse adjacency matrices given by edge indices and edge attributes to a single dense batched adjacency matrix. to_nested_tensor Given a contiguous batch of tensors $$\mathbf{X} \in \mathbb{R}^{(N_1 + \ldots + N_B) \times *}$$ (with $$N_i$$ indicating the number of elements in example $$i$$), creates a nested PyTorch tensor. from_nested_tensor Given a nested PyTorch tensor, creates a contiguous batch of tensors $$\mathbf{X} \in \mathbb{R}^{(N_1 + \ldots + N_B) \times *}$$, and optionally a batch vector which assigns each element to a specific example. dense_to_sparse Converts a dense adjacency matrix to a sparse adjacency matrix defined by edge indices and edge attributes. is_torch_sparse_tensor Returns True if the input src is a torch.sparse.Tensor (in any sparse layout). is_sparse Returns True if the input src is of type torch.sparse.Tensor (in any sparse layout) or of type torch_sparse.SparseTensor. to_torch_coo_tensor Converts a sparse adjacency matrix defined by edge indices and edge attributes to a torch.sparse.Tensor with layout torch.sparse_coo. to_torch_csr_tensor Converts a sparse adjacency matrix defined by edge indices and edge attributes to a torch.sparse.Tensor with layout torch.sparse_csr. to_torch_csc_tensor Converts a sparse adjacency matrix defined by edge indices and edge attributes to a torch.sparse.Tensor with layout torch.sparse_csc. to_torch_sparse_tensor Converts a sparse adjacency matrix defined by edge indices and edge attributes to a torch.sparse.Tensor with custom layout. to_edge_index Converts a torch.sparse.Tensor or a torch_sparse.SparseTensor to edge indices and edge attributes. spmm Matrix product of sparse matrix with dense matrix. unbatch Splits src according to a batch vector along dimension dim. unbatch_edge_index Splits the edge_index according to a batch vector. one_hot Taskes a one-dimensional index tensor and returns a one-hot encoded representation of it with shape [*, num_classes] that has zeros everywhere except where the index of last dimension matches the corresponding value of the input tensor, in which case it will be 1. normalized_cut Computes the normalized cut $$\mathbf{e}_{i,j} \cdot \left( \frac{1}{\deg(i)} + \frac{1}{\deg(j)} \right)$$ of a weighted graph given by edge indices and edge attributes. grid Returns the edge indices of a two-dimensional grid graph with height height and width width and its node positions. geodesic_distance Computes (normalized) geodesic distances of a mesh given by pos and face. to_scipy_sparse_matrix Converts a graph given by edge indices and edge attributes to a scipy sparse matrix. from_scipy_sparse_matrix Converts a scipy sparse matrix to edge indices and edge attributes. to_networkx Converts a torch_geometric.data.Data instance to a networkx.Graph if to_undirected is set to True, or a directed networkx.DiGraph otherwise. from_networkx Converts a networkx.Graph or networkx.DiGraph to a torch_geometric.data.Data instance. to_networkit Converts a (edge_index, edge_weight) tuple to a networkit.Graph. from_networkit Converts a networkit.Graph to a (edge_index, edge_weight) tuple. to_trimesh Converts a torch_geometric.data.Data instance to a trimesh.Trimesh. from_trimesh Converts a trimesh.Trimesh to a torch_geometric.data.Data instance. to_cugraph Converts a graph given by edge_index and optional edge_weight into a cugraph graph object. from_cugraph Converts a cugraph graph object into edge_index and optional edge_weight tensors. to_dgl Converts a torch_geometric.data.Data or torch_geometric.data.HeteroData instance to a dgl graph object. from_dgl Converts a dgl graph object to a torch_geometric.data.Data or torch_geometric.data.HeteroData instance. from_smiles Converts a SMILES string to a torch_geometric.data.Data instance. to_smiles Converts a torch_geometric.data.Data instance to a SMILES string. erdos_renyi_graph Returns the edge_index of a random Erdos-Renyi graph. stochastic_blockmodel_graph Returns the edge_index of a stochastic blockmodel graph. barabasi_albert_graph Returns the edge_index of a Barabasi-Albert preferential attachment model, where a graph of num_nodes nodes grows by attaching new nodes with num_edges edges that are preferentially attached to existing nodes with high degree. negative_sampling Samples random negative edges of a graph given by edge_index. batched_negative_sampling Samples random negative edges of multiple graphs given by edge_index and batch. structured_negative_sampling Samples a negative edge (i,k) for every positive edge (i,j) in the graph given by edge_index, and returns it as a tuple of the form (i,j,k). shuffle_node Randomly shuffle the feature matrix x along the first dimmension. mask_feature Randomly masks feature from the feature matrix x with probability p using samples from a Bernoulli distribution. add_random_edge Randomly adds edges to edge_index. tree_decomposition The tree decomposition algorithm of molecules from the "Junction Tree Variational Autoencoder for Molecular Graph Generation" paper. get_embeddings Returns the output embeddings of all MessagePassing layers in model. trim_to_layer Trims the edge_index representation, node features x and edge features edge_attr to a minimal-sized representation for the current GNN layer layer in directed NeighborLoader scenarios. get_ppr Calculates the personalized PageRank (PPR) vector for all or a subset of nodes using a variant of the Andersen algorithm. train_test_split_edges Splits the edges of a torch_geometric.data.Data object into positive and negative train/val/test edges.

Utility package.

scatter(src: Tensor, index: Tensor, dim: int = 0, dim_size: = None, reduce: str = 'sum') [source]

Reduces all values from the src tensor at the indices specified in the index tensor along a given dimension dim. See the documentation of the torch_scatter package for more information.

Parameters:
• src (torch.Tensor) – The source tensor.

• index (torch.Tensor) – The index tensor.

• dim (int, optional) – The dimension along which to index. (default: 0)

• dim_size (int, optional) – The size of the output tensor at dimension dim. If set to None, will create a minimal-sized output tensor according to index.max() + 1. (default: None)

• reduce (str, optional) – The reduce operation ("sum", "mean", "mul", "min" or "max", "any"). (default: "sum")

group_argsort(src: Tensor, index: Tensor, dim: int = 0, num_groups: = None, descending: bool = False, return_consecutive: bool = False, stable: bool = False) [source]

Returns the indices that sort the tensor src along a given dimension in ascending order by value. In contrast to torch.argsort(), sorting is performed in groups according to the values in index.

Parameters:
• src (torch.Tensor) – The source tensor.

• index (torch.Tensor) – The index tensor.

• dim (int, optional) – The dimension along which to index. (default: 0)

• num_groups (int, optional) – The number of groups. (default: None)

• descending (bool, optional) – Controls the sorting order (ascending or descending). (default: False)

• return_consecutive (bool, optional) – If set to True, will not offset the output to start from 0 for each group. (default: False)

• stable (bool, optional) – Controls the relative order of equivalent elements. (default: False)

Example

>>> src = torch.tensor([0, 1, 5, 4, 3, 2, 6, 7, 8])
>>> index = torch.tensor([0, 0, 1, 1, 1, 1, 2, 2, 2])
>>> group_argsort(src, index)
tensor([0, 1, 3, 2, 1, 0, 0, 1, 2])
segment(src: Tensor, ptr: Tensor, reduce: str = 'sum') [source]

Reduces all values in the first dimension of the src tensor within the ranges specified in the ptr. See the documentation of the torch_scatter package for more information.

Parameters:
• src (torch.Tensor) – The source tensor.

• ptr (torch.Tensor) – A monotonically increasing pointer tensor that refers to the boundaries of segments such that ptr[0] = 0 and ptr[-1] = src.size(0).

• reduce (str, optional) – The reduce operation ("sum", "mean", "min" or "max"). (default: "sum")

index_sort(inputs: Tensor, max_value: = None, stable: bool = False) [source]

Sorts the elements of the inputs tensor in ascending order. It is expected that inputs is one-dimensional and that it only contains positive integer values. If max_value is given, it can be used by the underlying algorithm for better performance.

Parameters:
• inputs (torch.Tensor) – A vector with positive integer values.

• max_value (int, optional) – The maximum value stored inside inputs. This value can be an estimation, but needs to be greater than or equal to the real maximum. (default: None)

• stable (bool, optional) – Makes the sorting routine stable, which guarantees that the order of equivalent elements is preserved. (default: False)

cumsum(x: Tensor, dim: int = 0) [source]

Returns the cumulative sum of elements of x. In contrast to torch.cumsum(), prepends the output with zero.

Parameters:
• x (torch.Tensor) – The input tensor.

• dim (int, optional) – The dimension to do the operation over. (default: 0)

Example

>>> x = torch.tensor([2, 4, 1])
>>> cumsum(x)
tensor([0, 2, 6, 7])
degree(index: Tensor, num_nodes: = None, dtype: = None) [source]

Computes the (unweighted) degree of a given one-dimensional index tensor.

Parameters:
• index (LongTensor) – Index tensor.

• num_nodes (int, optional) – The number of nodes, i.e. max_val + 1 of index. (default: None)

• dtype (torch.dtype, optional) – The desired data type of the returned tensor.

Return type:

Tensor

Example

>>> row = torch.tensor([0, 1, 0, 2, 0])
>>> degree(row, dtype=torch.long)
tensor([3, 1, 1])
softmax(src: Tensor, index: = None, ptr: = None, num_nodes: = None, dim: int = 0) [source]

Computes a sparsely evaluated softmax. Given a value tensor src, this function first groups the values along the first dimension based on the indices specified in index, and then proceeds to compute the softmax individually for each group.

Parameters:
• src (Tensor) – The source tensor.

• index (LongTensor, optional) – The indices of elements for applying the softmax. (default: None)

• ptr (LongTensor, optional) – If given, computes the softmax based on sorted inputs in CSR representation. (default: None)

• num_nodes (int, optional) – The number of nodes, i.e. max_val + 1 of index. (default: None)

• dim (int, optional) – The dimension in which to normalize. (default: 0)

Return type:

Tensor

Examples

>>> src = torch.tensor([1., 1., 1., 1.])
>>> index = torch.tensor([0, 0, 1, 2])
>>> ptr = torch.tensor([0, 2, 3, 4])
>>> softmax(src, index)
tensor([0.5000, 0.5000, 1.0000, 1.0000])
>>> softmax(src, None, ptr)
tensor([0.5000, 0.5000, 1.0000, 1.0000])
>>> src = torch.randn(4, 4)
>>> ptr = torch.tensor([0, 4])
>>> softmax(src, index, dim=-1)
tensor([[0.7404, 0.2596, 1.0000, 1.0000],
[0.1702, 0.8298, 1.0000, 1.0000],
[0.7607, 0.2393, 1.0000, 1.0000],
[0.8062, 0.1938, 1.0000, 1.0000]])
lexsort(keys: , dim: int = -1, descending: bool = False) [source]

Performs an indirect stable sort using a sequence of keys.

Given multiple sorting keys, returns an array of integer indices that describe their sort order. The last key in the sequence is used for the primary sort order, the second-to-last key for the secondary sort order, and so on.

Parameters:
• keys ([torch.Tensor]) – The $$k$$ different columns to be sorted. The last key is the primary sort key.

• dim (int, optional) – The dimension to sort along. (default: -1)

• descending (bool, optional) – Controls the sorting order (ascending or descending). (default: False)

sort_edge_index(edge_index: Tensor, edge_attr: Union[Tensor, None, List[Tensor], str] = '???', num_nodes: = None, sort_by_row: bool = True) [source]

Row-wise sorts edge_index.

Parameters:
• edge_index (torch.Tensor) – The edge indices.

• edge_attr (torch.Tensor or List[torch.Tensor], optional) – Edge weights or multi-dimensional edge features. If given as a list, will re-shuffle and remove duplicates for all its entries. (default: None)

• num_nodes (int, optional) – The number of nodes, i.e. max_val + 1 of edge_index. (default: None)

• sort_by_row (bool, optional) – If set to False, will sort edge_index column-wise/by destination node. (default: True)

Return type:

LongTensor if edge_attr is not passed, else (LongTensor, Optional[Tensor] or List[Tensor]])

Warning

From onwards, this function will always return a tuple whenever edge_attr is passed as an argument (even in case it is set to None).

Examples

>>> edge_index = torch.tensor([[2, 1, 1, 0],
[1, 2, 0, 1]])
>>> edge_attr = torch.tensor([[1], [2], [3], [4]])
>>> sort_edge_index(edge_index)
tensor([[0, 1, 1, 2],
[1, 0, 2, 1]])
>>> sort_edge_index(edge_index, edge_attr)
(tensor([[0, 1, 1, 2],
[1, 0, 2, 1]]),
tensor([[4],
[3],
[2],
[1]]))
coalesce(edge_index: Tensor, edge_attr: Union[Tensor, None, List[Tensor], str] = '???', num_nodes: = None, reduce: str = 'sum', is_sorted: bool = False, sort_by_row: bool = True) [source]

Row-wise sorts edge_index and removes its duplicated entries. Duplicate entries in edge_attr are merged by scattering them together according to the given reduce option.

Parameters:
• edge_index (torch.Tensor) – The edge indices.

• edge_attr (torch.Tensor or List[torch.Tensor], optional) – Edge weights or multi-dimensional edge features. If given as a list, will re-shuffle and remove duplicates for all its entries. (default: None)

• num_nodes (int, optional) – The number of nodes, i.e. max_val + 1 of edge_index. (default: None)

• reduce (str, optional) – The reduce operation to use for merging edge features ("sum", "mean", "min", "max", "mul", "any"). (default: "sum")

• is_sorted (bool, optional) – If set to True, will expect edge_index to be already sorted row-wise.

• sort_by_row (bool, optional) – If set to False, will sort edge_index column-wise.

Return type:

LongTensor if edge_attr is not passed, else (LongTensor, Optional[Tensor] or List[Tensor]])

Warning

From onwards, this function will always return a tuple whenever edge_attr is passed as an argument (even in case it is set to None).

Example

>>> edge_index = torch.tensor([[1, 1, 2, 3],
...                            [3, 3, 1, 2]])
>>> edge_attr = torch.tensor([1., 1., 1., 1.])
>>> coalesce(edge_index)
tensor([[1, 2, 3],
[3, 1, 2]])
>>> # Sort edge_index column-wise
>>> coalesce(edge_index, sort_by_row=False)
tensor([[2, 3, 1],
[1, 2, 3]])
>>> coalesce(edge_index, edge_attr)
(tensor([[1, 2, 3],
[3, 1, 2]]),
tensor([2., 1., 1.]))
>>> # Use 'mean' operation to merge edge features
>>> coalesce(edge_index, edge_attr, reduce='mean')
(tensor([[1, 2, 3],
[3, 1, 2]]),
tensor([1., 1., 1.]))
is_undirected(edge_index: Tensor, edge_attr: = None, num_nodes: = None) bool[source]

Returns True if the graph given by edge_index is undirected.

Parameters:
• edge_index (LongTensor) – The edge indices.

• edge_attr (Tensor or List[Tensor], optional) – Edge weights or multi- dimensional edge features. If given as a list, will check for equivalence in all its entries. (default: None)

• num_nodes (int, optional) – The number of nodes, i.e. max(edge_index) + 1. (default: None)

Return type:

bool

Examples

>>> edge_index = torch.tensor([[0, 1, 0],
...                         [1, 0, 0]])
>>> weight = torch.tensor([0, 0, 1])
>>> is_undirected(edge_index, weight)
True
>>> weight = torch.tensor([0, 1, 1])
>>> is_undirected(edge_index, weight)
False
to_undirected(edge_index: Tensor, edge_attr: Union[Tensor, None, List[Tensor], str] = '???', num_nodes: = None, reduce: str = 'add') [source]

Converts the graph given by edge_index to an undirected graph such that $$(j,i) \in \mathcal{E}$$ for every edge $$(i,j) \in \mathcal{E}$$.

Parameters:
• edge_index (LongTensor) – The edge indices.

• edge_attr (Tensor or List[Tensor], optional) – Edge weights or multi- dimensional edge features. If given as a list, will remove duplicates for all its entries. (default: None)

• num_nodes (int, optional) – The number of nodes, i.e. max(edge_index) + 1. (default: None)

• reduce (str, optional) – The reduce operation to use for merging edge features ("add", "mean", "min", "max", "mul"). (default: "add")

Return type:

LongTensor if edge_attr is not passed, else (LongTensor, Optional[Tensor] or List[Tensor]])

Warning

From onwards, this function will always return a tuple whenever edge_attr is passed as an argument (even in case it is set to None).

Examples

>>> edge_index = torch.tensor([[0, 1, 1],
...                            [1, 0, 2]])
>>> to_undirected(edge_index)
tensor([[0, 1, 1, 2],
[1, 0, 2, 1]])
>>> edge_index = torch.tensor([[0, 1, 1],
...                            [1, 0, 2]])
>>> edge_weight = torch.tensor([1., 1., 1.])
>>> to_undirected(edge_index, edge_weight)
(tensor([[0, 1, 1, 2],
[1, 0, 2, 1]]),
tensor([2., 2., 1., 1.]))
>>> # Use 'mean' operation to merge edge features
>>>  to_undirected(edge_index, edge_weight, reduce='mean')
(tensor([[0, 1, 1, 2],
[1, 0, 2, 1]]),
tensor([1., 1., 1., 1.]))
contains_self_loops(edge_index: Tensor) bool[source]

Returns True if the graph given by edge_index contains self-loops.

Parameters:

edge_index (LongTensor) – The edge indices.

Return type:

bool

Examples

>>> edge_index = torch.tensor([[0, 1, 0],
...                            [1, 0, 0]])
>>> contains_self_loops(edge_index)
True
>>> edge_index = torch.tensor([[0, 1, 1],
...                            [1, 0, 2]])
>>> contains_self_loops(edge_index)
False
remove_self_loops(edge_index: Tensor, edge_attr: = None) [source]

Removes every self-loop in the graph given by edge_index, so that $$(i,i) \not\in \mathcal{E}$$ for every $$i \in \mathcal{V}$$.

Parameters:
• edge_index (LongTensor) – The edge indices.

• edge_attr (Tensor, optional) – Edge weights or multi-dimensional edge features. (default: None)

Return type:

(LongTensor, Tensor)

Example

>>> edge_index = torch.tensor([[0, 1, 0],
...                            [1, 0, 0]])
>>> edge_attr = [[1, 2], [3, 4], [5, 6]]
>>> edge_attr = torch.tensor(edge_attr)
>>> remove_self_loops(edge_index, edge_attr)
(tensor([[0, 1],
[1, 0]]),
tensor([[1, 2],
[3, 4]]))
segregate_self_loops(edge_index: Tensor, edge_attr: = None) [source]

Segregates self-loops from the graph.

Parameters:
• edge_index (LongTensor) – The edge indices.

• edge_attr (Tensor, optional) – Edge weights or multi-dimensional edge features. (default: None)

Return type:

(LongTensor, Tensor, LongTensor, Tensor)

Example

>>> edge_index = torch.tensor([[0, 0, 1],
...                            [0, 1, 0]])
>>> (edge_index, edge_attr,
...  loop_edge_index,
...  loop_edge_attr) = segregate_self_loops(edge_index)
>>>  loop_edge_index
tensor([[0],
[0]])
add_self_loops(edge_index: Tensor, edge_attr: = None, fill_value: = None, num_nodes: Optional[Union[int, Tuple[int, int]]] = None) [source]

Adds a self-loop $$(i,i) \in \mathcal{E}$$ to every node $$i \in \mathcal{V}$$ in the graph given by edge_index. In case the graph is weighted or has multi-dimensional edge features (edge_attr != None), edge features of self-loops will be added according to fill_value.

Parameters:
• edge_index (LongTensor) – The edge indices.

• edge_attr (Tensor, optional) – Edge weights or multi-dimensional edge features. (default: None)

• fill_value (float or Tensor or str, optional) – The way to generate edge features of self-loops (in case edge_attr != None). If given as float or torch.Tensor, edge features of self-loops will be directly given by fill_value. If given as str, edge features of self-loops are computed by aggregating all features of edges that point to the specific node, according to a reduce operation. ("add", "mean", "min", "max", "mul"). (default: 1.)

• num_nodes (int or Tuple[int, int], optional) – The number of nodes, i.e. max_val + 1 of edge_index. If given as a tuple, then edge_index is interpreted as a bipartite graph with shape (num_src_nodes, num_dst_nodes). (default: None)

Return type:

(LongTensor, Tensor)

Examples

>>> edge_index = torch.tensor([[0, 1, 0],
...                            [1, 0, 0]])
>>> edge_weight = torch.tensor([0.5, 0.5, 0.5])
(tensor([[0, 1, 0, 0, 1],
[1, 0, 0, 0, 1]]),
None)
(tensor([[0, 1, 0, 0, 1],
[1, 0, 0, 0, 1]]),
tensor([0.5000, 0.5000, 0.5000, 1.0000, 1.0000]))
>>> # edge features of self-loops are filled by constant 2.0
...                fill_value=2.)
(tensor([[0, 1, 0, 0, 1],
[1, 0, 0, 0, 1]]),
tensor([0.5000, 0.5000, 0.5000, 2.0000, 2.0000]))
>>> # Use 'add' operation to merge edge features for self-loops
(tensor([[0, 1, 0, 0, 1],
[1, 0, 0, 0, 1]]),
tensor([0.5000, 0.5000, 0.5000, 1.0000, 0.5000]))
add_remaining_self_loops(edge_index: Tensor, edge_attr: = None, fill_value: = None, num_nodes: = None) [source]

Adds remaining self-loop $$(i,i) \in \mathcal{E}$$ to every node $$i \in \mathcal{V}$$ in the graph given by edge_index. In case the graph is weighted or has multi-dimensional edge features (edge_attr != None), edge features of non-existing self-loops will be added according to fill_value.

Parameters:
• edge_index (LongTensor) – The edge indices.

• edge_attr (Tensor, optional) – Edge weights or multi-dimensional edge features. (default: None)

• fill_value (float or Tensor or str, optional) – The way to generate edge features of self-loops (in case edge_attr != None). If given as float or torch.Tensor, edge features of self-loops will be directly given by fill_value. If given as str, edge features of self-loops are computed by aggregating all features of edges that point to the specific node, according to a reduce operation. ("add", "mean", "min", "max", "mul"). (default: 1.)

• num_nodes (int, optional) – The number of nodes, i.e. max_val + 1 of edge_index. (default: None)

Return type:

(LongTensor, Tensor)

Example

>>> edge_index = torch.tensor([[0, 1],
...                            [1, 0]])
>>> edge_weight = torch.tensor([0.5, 0.5])
(tensor([[0, 1, 0, 1],
[1, 0, 0, 1]]),
tensor([0.5000, 0.5000, 1.0000, 1.0000]))
get_self_loop_attr(edge_index: Tensor, edge_attr: = None, num_nodes: = None) [source]

Returns the edge features or weights of self-loops $$(i, i)$$ of every node $$i \in \mathcal{V}$$ in the graph given by edge_index. Edge features of missing self-loops not present in edge_index will be filled with zeros. If edge_attr is not given, it will be the vector of ones.

Note

This operation is analogous to getting the diagonal elements of the dense adjacency matrix.

Parameters:
• edge_index (LongTensor) – The edge indices.

• edge_attr (Tensor, optional) – Edge weights or multi-dimensional edge features. (default: None)

• num_nodes (int, optional) – The number of nodes, i.e. max_val + 1 of edge_index. (default: None)

Return type:

Tensor

Examples

>>> edge_index = torch.tensor([[0, 1, 0],
...                            [1, 0, 0]])
>>> edge_weight = torch.tensor([0.2, 0.3, 0.5])
>>> get_self_loop_attr(edge_index, edge_weight)
tensor([0.5000, 0.0000])
>>> get_self_loop_attr(edge_index, edge_weight, num_nodes=4)
tensor([0.5000, 0.0000, 0.0000, 0.0000])
contains_isolated_nodes(edge_index: Tensor, num_nodes: = None) bool[source]

Returns True if the graph given by edge_index contains isolated nodes.

Parameters:
• edge_index (LongTensor) – The edge indices.

• num_nodes (int, optional) – The number of nodes, i.e. max_val + 1 of edge_index. (default: None)

Return type:

bool

Examples

>>> edge_index = torch.tensor([[0, 1, 0],
...                            [1, 0, 0]])
>>> contains_isolated_nodes(edge_index)
False
>>> contains_isolated_nodes(edge_index, num_nodes=3)
True
remove_isolated_nodes(edge_index: Tensor, edge_attr: = None, num_nodes: = None) [source]

Removes the isolated nodes from the graph given by edge_index with optional edge attributes edge_attr. In addition, returns a mask of shape [num_nodes] to manually filter out isolated node features later on. Self-loops are preserved for non-isolated nodes.

Parameters:
• edge_index (LongTensor) – The edge indices.

• edge_attr (Tensor, optional) – Edge weights or multi-dimensional edge features. (default: None)

• num_nodes (int, optional) – The number of nodes, i.e. max_val + 1 of edge_index. (default: None)

Return type:

(LongTensor, Tensor, BoolTensor)

Examples

>>> edge_index = torch.tensor([[0, 1, 0],
...                            [1, 0, 0]])
>>> edge_index, edge_attr, mask = remove_isolated_nodes(edge_index)
tensor([True, True])
>>> edge_index, edge_attr, mask = remove_isolated_nodes(edge_index,
...                                                     num_nodes=3)
tensor([True, True, False])
get_num_hops(model: Module) int[source]

Returns the number of hops the model is aggregating information from.

Note

This function counts the number of message passing layers as an approximation of the total number of hops covered by the model. Its output may not necessarily be correct in case message passing layers perform multi-hop aggregation, e.g., as in ChebConv.

Example

>>> class GNN(torch.nn.Module):
...     def __init__(self):
...         super().__init__()
...         self.conv1 = GCNConv(3, 16)
...         self.conv2 = GCNConv(16, 16)
...         self.lin = Linear(16, 2)
...
...     def forward(self, x, edge_index):
...         x = self.conv1(x, edge_index).relu()
...         x = self.conv2(x, edge_index).relu()
...         return self.lin(x)
>>> get_num_hops(GNN())
2
subgraph(subset: Union[Tensor, List[int]], edge_index: Tensor, edge_attr: = None, relabel_nodes: bool = False, num_nodes: = None, *, return_edge_mask: bool = False) [source]

Returns the induced subgraph of (edge_index, edge_attr) containing the nodes in subset.

Parameters:
• subset (LongTensor, BoolTensor or [int]) – The nodes to keep.

• edge_index (LongTensor) – The edge indices.

• edge_attr (Tensor, optional) – Edge weights or multi-dimensional edge features. (default: None)

• relabel_nodes (bool, optional) – If set to True, the resulting edge_index will be relabeled to hold consecutive indices starting from zero. (default: False)

• num_nodes (int, optional) – The number of nodes, i.e. max(edge_index) + 1. (default: None)

• return_edge_mask (bool, optional) – If set to True, will return the edge mask to filter out additional edge features. (default: False)

Return type:

(LongTensor, Tensor)

Examples

>>> edge_index = torch.tensor([[0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6],
...                            [1, 0, 2, 1, 3, 2, 4, 3, 5, 4, 6, 5]])
>>> edge_attr = torch.tensor([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12])
>>> subset = torch.tensor([3, 4, 5])
>>> subgraph(subset, edge_index, edge_attr)
(tensor([[3, 4, 4, 5],
[4, 3, 5, 4]]),
tensor([ 7.,  8.,  9., 10.]))
(tensor([[3, 4, 4, 5],
[4, 3, 5, 4]]),
tensor([ 7.,  8.,  9., 10.]),
tensor([False, False, False, False, False, False,  True,
True,  True,  True,  False, False]))
bipartite_subgraph(subset: Union[Tuple[Tensor, Tensor], Tuple[List[int], List[int]]], edge_index: Tensor, edge_attr: = None, relabel_nodes: bool = False, size: Optional[Tuple[int, int]] = None, return_edge_mask: bool = False) [source]

Returns the induced subgraph of the bipartite graph (edge_index, edge_attr) containing the nodes in subset.

Parameters:
• subset (Tuple[Tensor, Tensor] or tuple([int],[int])) – The nodes to keep.

• edge_index (LongTensor) – The edge indices.

• edge_attr (Tensor, optional) – Edge weights or multi-dimensional edge features. (default: None)

• relabel_nodes (bool, optional) – If set to True, the resulting edge_index will be relabeled to hold consecutive indices starting from zero. (default: False)

• size (tuple, optional) – The number of nodes. (default: None)

• return_edge_mask (bool, optional) – If set to True, will return the edge mask to filter out additional edge features. (default: False)

Return type:

(LongTensor, Tensor)

Examples

>>> edge_index = torch.tensor([[0, 5, 2, 3, 3, 4, 4, 3, 5, 5, 6],
...                            [0, 0, 3, 2, 0, 0, 2, 1, 2, 3, 1]])
>>> edge_attr = torch.tensor([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])
>>> subset = (torch.tensor([2, 3, 5]), torch.tensor([2, 3]))
>>> bipartite_subgraph(subset, edge_index, edge_attr)
(tensor([[2, 3, 5, 5],
[3, 2, 2, 3]]),
tensor([ 3,  4,  9, 10]))
>>> bipartite_subgraph(subset, edge_index, edge_attr,
(tensor([[2, 3, 5, 5],
[3, 2, 2, 3]]),
tensor([ 3,  4,  9, 10]),
tensor([False, False,  True,  True, False, False, False, False,
True,  True,  False]))
k_hop_subgraph(node_idx: Union[int, List[int], Tensor], num_hops: int, edge_index: Tensor, relabel_nodes: bool = False, num_nodes: = None, flow: str = 'source_to_target', directed: bool = False) [source]

Computes the induced subgraph of edge_index around all nodes in node_idx reachable within $$k$$ hops.

The flow argument denotes the direction of edges for finding $$k$$-hop neighbors. If set to "source_to_target", then the method will find all neighbors that point to the initial set of seed nodes in node_idx. This mimics the natural flow of message passing in Graph Neural Networks.

The method returns (1) the nodes involved in the subgraph, (2) the filtered edge_index connectivity, (3) the mapping from node indices in node_idx to their new location, and (4) the edge mask indicating which edges were preserved.

Parameters:
• node_idx (int, list, tuple or torch.Tensor) – The central seed node(s).

• num_hops (int) – The number of hops $$k$$.

• edge_index (LongTensor) – The edge indices.

• relabel_nodes (bool, optional) – If set to True, the resulting edge_index will be relabeled to hold consecutive indices starting from zero. (default: False)

• num_nodes (int, optional) – The number of nodes, i.e. max_val + 1 of edge_index. (default: None)

• flow (str, optional) – The flow direction of $$k$$-hop aggregation ("source_to_target" or "target_to_source"). (default: "source_to_target")

• directed (bool, optional) – If set to True, will only include directed edges to the seed nodes node_idx. (default: False)

Return type:

(LongTensor, LongTensor, LongTensor, BoolTensor)

Examples

>>> edge_index = torch.tensor([[0, 1, 2, 3, 4, 5],
...                            [2, 2, 4, 4, 6, 6]])
>>> # Center node 6, 2-hops
>>> subset, edge_index, mapping, edge_mask = k_hop_subgraph(
...     6, 2, edge_index, relabel_nodes=True)
>>> subset
tensor([2, 3, 4, 5, 6])
>>> edge_index
tensor([[0, 1, 2, 3],
[2, 2, 4, 4]])
>>> mapping
tensor([4])
tensor([False, False,  True,  True,  True,  True])
>>> subset[mapping]
tensor([6])
>>> edge_index = torch.tensor([[1, 2, 4, 5],
...                            [0, 1, 5, 6]])
>>> (subset, edge_index,
...  mapping, edge_mask) = k_hop_subgraph([0, 6], 2,
...                                       edge_index,
...                                       relabel_nodes=True)
>>> subset
tensor([0, 1, 2, 4, 5, 6])
>>> edge_index
tensor([[1, 2, 3, 4],
[0, 1, 4, 5]])
>>> mapping
tensor([0, 5])
tensor([True, True, True, True])
>>> subset[mapping]
tensor([0, 6])
dropout_node(edge_index: Tensor, p: float = 0.5, num_nodes: = None, training: bool = True, relabel_nodes: bool = False) [source]

Randomly drops nodes from the adjacency matrix edge_index with probability p using samples from a Bernoulli distribution.

The method returns (1) the retained edge_index, (2) the edge mask indicating which edges were retained. (3) the node mask indicating which nodes were retained.

Parameters:
• edge_index (LongTensor) – The edge indices.

• p (float, optional) – Dropout probability. (default: 0.5)

• num_nodes (int, optional) – The number of nodes, i.e. max_val + 1 of edge_index. (default: None)

• training (bool, optional) – If set to False, this operation is a no-op. (default: True)

• relabel_nodes (bool, optional) – If set to True, the resulting edge_index will be relabeled to hold consecutive indices starting from zero.

Return type:

(LongTensor, BoolTensor, BoolTensor)

Examples

>>> edge_index = torch.tensor([[0, 1, 1, 2, 2, 3],
...                            [1, 0, 2, 1, 3, 2]])
>>> edge_index
tensor([[0, 1],
[1, 0]])
tensor([ True,  True, False, False, False, False])
tensor([ True,  True, False, False])
dropout_edge(edge_index: Tensor, p: float = 0.5, force_undirected: bool = False, training: bool = True) [source]

Randomly drops edges from the adjacency matrix edge_index with probability p using samples from a Bernoulli distribution.

The method returns (1) the retained edge_index, (2) the edge mask or index indicating which edges were retained, depending on the argument force_undirected.

Parameters:
• edge_index (LongTensor) – The edge indices.

• p (float, optional) – Dropout probability. (default: 0.5)

• force_undirected (bool, optional) – If set to True, will either drop or keep both edges of an undirected edge. (default: False)

• training (bool, optional) – If set to False, this operation is a no-op. (default: True)

Return type:

(LongTensor, BoolTensor or LongTensor)

Examples

>>> edge_index = torch.tensor([[0, 1, 1, 2, 2, 3],
...                            [1, 0, 2, 1, 3, 2]])
>>> edge_index
tensor([[0, 1, 2, 2],
[1, 2, 1, 3]])
tensor([ True, False,  True,  True,  True, False])
>>> edge_index, edge_id = dropout_edge(edge_index,
...                                    force_undirected=True)
>>> edge_index
tensor([[0, 1, 2, 1, 2, 3],
[1, 2, 3, 0, 1, 2]])
>>> edge_id # indices indicating which edges are retained
tensor([0, 2, 4, 0, 2, 4])
dropout_path(edge_index: Tensor, p: float = 0.2, walks_per_node: int = 1, walk_length: int = 3, num_nodes: = None, is_sorted: bool = False, training: bool = True) [source]

Drops edges from the adjacency matrix edge_index based on random walks. The source nodes to start random walks from are sampled from edge_index with probability p, following a Bernoulli distribution.

The method returns (1) the retained edge_index, (2) the edge mask indicating which edges were retained.

Parameters:
• edge_index (LongTensor) – The edge indices.

• p (float, optional) – Sample probability. (default: 0.2)

• walks_per_node (int, optional) – The number of walks per node, same as Node2Vec. (default: 1)

• walk_length (int, optional) – The walk length, same as Node2Vec. (default: 3)

• num_nodes (int, optional) – The number of nodes, i.e. max_val + 1 of edge_index. (default: None)

• is_sorted (bool, optional) – If set to True, will expect edge_index to be already sorted row-wise. (default: False)

• training (bool, optional) – If set to False, this operation is a no-op. (default: True)

Return type:

(LongTensor, BoolTensor)

Example

>>> edge_index = torch.tensor([[0, 1, 1, 2, 2, 3],
...                            [1, 0, 2, 1, 3, 2]])
>>> edge_index
tensor([[1, 2],
[2, 3]])
tensor([False, False,  True, False,  True, False])
dropout_adj(edge_index: Tensor, edge_attr: = None, p: float = 0.5, force_undirected: bool = False, num_nodes: = None, training: bool = True) [source]

Randomly drops edges from the adjacency matrix (edge_index, edge_attr) with probability p using samples from a Bernoulli distribution.

Warning

dropout_adj is deprecated and will be removed in a future release. Use torch_geometric.utils.dropout_edge instead.

Parameters:
• edge_index (LongTensor) – The edge indices.

• edge_attr (Tensor, optional) – Edge weights or multi-dimensional edge features. (default: None)

• p (float, optional) – Dropout probability. (default: 0.5)

• force_undirected (bool, optional) – If set to True, will either drop or keep both edges of an undirected edge. (default: False)

• num_nodes (int, optional) – The number of nodes, i.e. max_val + 1 of edge_index. (default: None)

• training (bool, optional) – If set to False, this operation is a no-op. (default: True)

Examples

>>> edge_index = torch.tensor([[0, 1, 1, 2, 2, 3],
...                            [1, 0, 2, 1, 3, 2]])
>>> edge_attr = torch.tensor([1, 2, 3, 4, 5, 6])
(tensor([[0, 1, 2, 3],
[1, 2, 3, 2]]),
tensor([1, 3, 5, 6]))
>>> # The returned graph is kept undirected
(tensor([[0, 1, 2, 1, 2, 3],
[1, 2, 3, 0, 1, 2]]),
tensor([1, 3, 5, 1, 3, 5]))
homophily(edge_index: Union[Tensor, SparseTensor], y: Tensor, batch: = None, method: str = 'edge') [source]

The homophily of a graph characterizes how likely nodes with the same label are near each other in a graph.

There are many measures of homophily that fits this definition. In particular:

• In the “Beyond Homophily in Graph Neural Networks: Current Limitations and Effective Designs” paper, the homophily is the fraction of edges in a graph which connects nodes that have the same class label:

$\frac{| \{ (v,w) : (v,w) \in \mathcal{E} \wedge y_v = y_w \} | } {|\mathcal{E}|}$

That measure is called the edge homophily ratio.

• In the “Geom-GCN: Geometric Graph Convolutional Networks” paper, edge homophily is normalized across neighborhoods:

$\frac{1}{|\mathcal{V}|} \sum_{v \in \mathcal{V}} \frac{ | \{ (w,v) : w \in \mathcal{N}(v) \wedge y_v = y_w \} | } { |\mathcal{N}(v)| }$

That measure is called the node homophily ratio.

• In the “Large-Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods” paper, edge homophily is modified to be insensitive to the number of classes and size of each class:

$\frac{1}{C-1} \sum_{k=1}^{C} \max \left(0, h_k - \frac{|\mathcal{C}_k|} {|\mathcal{V}|} \right),$

where $$C$$ denotes the number of classes, $$|\mathcal{C}_k|$$ denotes the number of nodes of class $$k$$, and $$h_k$$ denotes the edge homophily ratio of nodes of class $$k$$.

Thus, that measure is called the class insensitive edge homophily ratio.

Parameters:
• edge_index (Tensor or SparseTensor) – The graph connectivity.

• y (Tensor) – The labels.

• batch (LongTensor, optional) – Batch vector$$\mathbf{b} \in {\{ 0, \ldots,B-1\}}^N$$, which assigns each node to a specific example. (default: None)

• method (str, optional) – The method used to calculate the homophily, either "edge" (first formula), "node" (second formula) or "edge_insensitive" (third formula). (default: "edge")

Examples

>>> edge_index = torch.tensor([[0, 1, 2, 3],
...                            [1, 2, 0, 4]])
>>> y = torch.tensor([0, 0, 0, 0, 1])
>>> # Edge homophily ratio
>>> homophily(edge_index, y, method='edge')
0.75
>>> # Node homophily ratio
>>> homophily(edge_index, y, method='node')
0.6000000238418579
>>> # Class insensitive edge homophily ratio
>>> homophily(edge_index, y, method='edge_insensitive')
0.19999998807907104
assortativity(edge_index: Union[Tensor, SparseTensor]) [source]

The degree assortativity coefficient from the “Mixing patterns in networks” paper. Assortativity in a network refers to the tendency of nodes to connect with other similar nodes over dissimilar nodes. It is computed from Pearson correlation coefficient of the node degrees.

Parameters:

edge_index (Tensor or SparseTensor) – The graph connectivity.

Returns:

The value of the degree assortativity coefficient for the input graph $$\in [-1, 1]$$

Example

>>> edge_index = torch.tensor([[0, 1, 2, 3, 2],
...                            [1, 2, 0, 1, 3]])
>>> assortativity(edge_index)
-0.666667640209198
get_laplacian(edge_index: Tensor, edge_weight: = None, normalization: = None, dtype: = None, num_nodes: = None) [source]

Computes the graph Laplacian of the graph given by edge_index and optional edge_weight.

Parameters:
• edge_index (LongTensor) – The edge indices.

• edge_weight (Tensor, optional) – One-dimensional edge weights. (default: None)

• normalization (str, optional) –

The normalization scheme for the graph Laplacian (default: None):

1. None: No normalization $$\mathbf{L} = \mathbf{D} - \mathbf{A}$$

2. "sym": Symmetric normalization $$\mathbf{L} = \mathbf{I} - \mathbf{D}^{-1/2} \mathbf{A} \mathbf{D}^{-1/2}$$

3. "rw": Random-walk normalization $$\mathbf{L} = \mathbf{I} - \mathbf{D}^{-1} \mathbf{A}$$

• dtype (torch.dtype, optional) – The desired data type of returned tensor in case edge_weight=None. (default: None)

• num_nodes (int, optional) – The number of nodes, i.e. max_val + 1 of edge_index. (default: None)

Examples

>>> edge_index = torch.tensor([[0, 1, 1, 2],
...                            [1, 0, 2, 1]])
>>> edge_weight = torch.tensor([1., 2., 2., 4.])
>>> # No normalization
>>> lap = get_laplacian(edge_index, edge_weight)
>>> # Symmetric normalization
>>> lap_sym = get_laplacian(edge_index, edge_weight,
normalization='sym')
>>> # Random-walk normalization
>>> lap_rw = get_laplacian(edge_index, edge_weight, normalization='rw')
get_mesh_laplacian(pos: Tensor, face: Tensor, normalization: = None) [source]

Computes the mesh Laplacian of a mesh given by pos and face.

Computation is based on the cotangent matrix defined as

$\begin{split}\mathbf{C}_{ij} = \begin{cases} \frac{\cot \angle_{ikj}~+\cot \angle_{ilj}}{2} & \text{if } i, j \text{ is an edge} \\ -\sum_{j \in N(i)}{C_{ij}} & \text{if } i \text{ is in the diagonal} \\ 0 & \text{otherwise} \end{cases}\end{split}$

Normalization depends on the mass matrix defined as

$\begin{split}\mathbf{M}_{ij} = \begin{cases} a(i) & \text{if } i \text{ is in the diagonal} \\ 0 & \text{otherwise} \end{cases}\end{split}$

where $$a(i)$$ is obtained by joining the barycenters of the triangles around vertex $$i$$.

Parameters:
• pos (Tensor) – The node positions.

• face (LongTensor) – The face indices.

• normalization (str, optional) –

The normalization scheme for the mesh Laplacian (default: None):

1. None: No normalization $$\mathbf{L} = \mathbf{C}$$

2. "sym": Symmetric normalization $$\mathbf{L} = \mathbf{M}^{-1/2} \mathbf{C}\mathbf{M}^{-1/2}$$

3. "rw": Row-wise normalization $$\mathbf{L} = \mathbf{M}^{-1} \mathbf{C}$$

Returns a new tensor which masks the src tensor along the dimension dim according to the boolean mask mask.

Parameters:
• src (torch.Tensor) – The input tensor.

• dim (int) – The dimension in which to mask.

• mask (torch.BoolTensor) – The 1-D tensor containing the binary mask to index with.

index_to_mask(index: Tensor, size: = None) [source]

Converts indices to a mask representation.

Parameters:
• index (Tensor) – The indices.

• size (int, optional) – The size of the mask. If set to None, a minimal sized output mask is returned.

Example

>>> index = torch.tensor([1, 3, 5])
tensor([False,  True, False,  True, False,  True])
tensor([False,  True, False,  True, False,  True, False])

Converts a mask to an index representation.

Parameters:

Example

>>> mask = torch.tensor([False, True, False])
tensor([1])
select(src: Union[Tensor, List[Any], TensorFrame], index_or_mask: Tensor, dim: int) Union[Tensor, List[Any]][source]

Selects the input tensor or input list according to a given index or mask vector.

Parameters:
• src (torch.Tensor or list) – The input tensor or list.

• dim (int) – The dimension along which to select.

narrow(src: Union[Tensor, List[Any]], dim: int, start: int, length: int) Union[Tensor, List[Any]][source]

Narrows the input tensor or input list to the specified range.

Parameters:
• src (torch.Tensor or list) – The input tensor or list.

• dim (int) – The dimension along which to narrow.

• start (int) – The starting dimension.

• length (int) – The distance to the ending dimension.

to_dense_batch(x: Tensor, batch: = None, fill_value: float = 0.0, max_num_nodes: = None, batch_size: = None) [source]

Given a sparse batch of node features $$\mathbf{X} \in \mathbb{R}^{(N_1 + \ldots + N_B) \times F}$$ (with $$N_i$$ indicating the number of nodes in graph $$i$$), creates a dense node feature tensor $$\mathbf{X} \in \mathbb{R}^{B \times N_{\max} \times F}$$ (with $$N_{\max} = \max_i^B N_i$$). In addition, a mask of shape $$\mathbf{M} \in \{ 0, 1 \}^{B \times N_{\max}}$$ is returned, holding information about the existence of fake-nodes in the dense representation.

Parameters:
• x (Tensor) – Node feature matrix $$\mathbf{X} \in \mathbb{R}^{(N_1 + \ldots + N_B) \times F}$$.

• batch (LongTensor, optional) – Batch vector $$\mathbf{b} \in {\{ 0, \ldots, B-1\}}^N$$, which assigns each node to a specific example. Must be ordered. (default: None)

• fill_value (float, optional) – The value for invalid entries in the resulting dense output tensor. (default: 0)

• max_num_nodes (int, optional) – The size of the output node dimension. (default: None)

• batch_size (int, optional) – The batch size. (default: None)

Return type:

(Tensor, BoolTensor)

Examples

>>> x = torch.arange(12).view(6, 2)
>>> x
tensor([[ 0,  1],
[ 2,  3],
[ 4,  5],
[ 6,  7],
[ 8,  9],
[10, 11]])
tensor([[True, True, True, True, True, True]])
>>> batch = torch.tensor([0, 0, 1, 2, 2, 2])
>>> out, mask = to_dense_batch(x, batch)
>>> out
tensor([[[ 0,  1],
[ 2,  3],
[ 0,  0]],
[[ 4,  5],
[ 0,  0],
[ 0,  0]],
[[ 6,  7],
[ 8,  9],
[10, 11]]])
tensor([[ True,  True, False],
[ True, False, False],
[ True,  True,  True]])
>>> out, mask = to_dense_batch(x, batch, max_num_nodes=4)
>>> out
tensor([[[ 0,  1],
[ 2,  3],
[ 0,  0],
[ 0,  0]],
[[ 4,  5],
[ 0,  0],
[ 0,  0],
[ 0,  0]],
[[ 6,  7],
[ 8,  9],
[10, 11],
[ 0,  0]]])
tensor([[ True,  True, False, False],
[ True, False, False, False],
[ True,  True,  True, False]])
to_dense_adj(edge_index: Tensor, batch: = None, edge_attr: = None, max_num_nodes: = None, batch_size: = None) [source]

Converts batched sparse adjacency matrices given by edge indices and edge attributes to a single dense batched adjacency matrix.

Parameters:
• edge_index (LongTensor) – The edge indices.

• batch (LongTensor, optional) – Batch vector $$\mathbf{b} \in {\{ 0, \ldots, B-1\}}^N$$, which assigns each node to a specific example. (default: None)

• edge_attr (Tensor, optional) – Edge weights or multi-dimensional edge features. If edge_index contains duplicated edges, the dense adjacency matrix output holds the summed up entries of edge_attr for duplicated edges. (default: None)

• max_num_nodes (int, optional) – The size of the output node dimension. (default: None)

• batch_size (int, optional) – The batch size. (default: None)

Return type:

Tensor

Examples

>>> edge_index = torch.tensor([[0, 0, 1, 2, 3],
...                            [0, 1, 0, 3, 0]])
>>> batch = torch.tensor([0, 0, 1, 1])
tensor([[[1., 1.],
[1., 0.]],
[[0., 1.],
[1., 0.]]])
tensor([[[1., 1., 0., 0.],
[1., 0., 0., 0.],
[0., 0., 0., 0.],
[0., 0., 0., 0.]],
[[0., 1., 0., 0.],
[1., 0., 0., 0.],
[0., 0., 0., 0.],
[0., 0., 0., 0.]]])
>>> edge_attr = torch.tensor([1.0, 2.0, 3.0, 4.0, 5.0])
tensor([[[1., 2.],
[3., 0.]],
[[0., 4.],
[5., 0.]]])
to_nested_tensor(x: Tensor, batch: = None, ptr: = None, batch_size: = None) [source]

Given a contiguous batch of tensors $$\mathbf{X} \in \mathbb{R}^{(N_1 + \ldots + N_B) \times *}$$ (with $$N_i$$ indicating the number of elements in example $$i$$), creates a nested PyTorch tensor. Reverse operation of from_nested_tensor().

Parameters:
• x (torch.Tensor) – The input tensor $$\mathbf{X} \in \mathbb{R}^{(N_1 + \ldots + N_B) \times *}$$.

• batch (torch.Tensor, optional) – The batch vector $$\mathbf{b} \in {\{ 0, \ldots, B-1\}}^N$$, which assigns each element to a specific example. Must be ordered. (default: None)

• ptr (torch.Tensor, optional) – Alternative representation of batch in compressed format. (default: None)

• batch_size (int, optional) – The batch size $$B$$. (default: None)

from_nested_tensor(x: Tensor, return_batch: bool = False) [source]

Given a nested PyTorch tensor, creates a contiguous batch of tensors $$\mathbf{X} \in \mathbb{R}^{(N_1 + \ldots + N_B) \times *}$$, and optionally a batch vector which assigns each element to a specific example. Reverse operation of to_nested_tensor().

Parameters:
• x (torch.Tensor) – The nested input tensor. The size of nested tensors need to match except for the first dimension.

• return_batch (bool, optional) – If set to True, will also return the batch vector $$\mathbf{b} \in {\{ 0, \ldots, B-1\}}^N$$. (default: False)

Converts a dense adjacency matrix to a sparse adjacency matrix defined by edge indices and edge attributes.

Parameters:
• adj (torch.Tensor) – The dense adjacency matrix of shape [num_nodes, num_nodes] or [batch_size, num_nodes, num_nodes].

• mask (torch.Tensor, optional) – A boolean tensor of shape [batch_size, num_nodes] holding information about which nodes are in each example are valid. (default: None)

Return type:

(LongTensor, Tensor)

Examples

>>> # For a single adjacency matrix:
...                     [2, 0]])
(tensor([[0, 0, 1],
[0, 1, 0]]),
tensor([3, 1, 2]))
>>> # For two adjacency matrixes:
...                      [2, 0]],
...                     [[0, 1],
...                      [0, 2]]])
(tensor([[0, 0, 1, 2, 3],
[0, 1, 0, 3, 3]]),
tensor([3, 1, 2, 1, 2]))
>>> # First graph with two nodes, second with three:
...         [3, 1, 0],
...         [2, 0, 0],
...         [0, 0, 0]
...     ], [
...         [0, 1, 0],
...         [0, 2, 3],
...         [0, 5, 0]
...     ]])
...         [True, True, False],
...         [True, True, True]
...     ])
(tensor([[0, 0, 1, 2, 3, 3, 4],
[0, 1, 0, 3, 3, 4, 3]]),
tensor([3, 1, 2, 1, 2, 3, 5]))
is_torch_sparse_tensor(src: Any) bool[source]

Returns True if the input src is a torch.sparse.Tensor (in any sparse layout).

Parameters:

src (Any) – The input object to be checked.

is_sparse(src: Any) bool[source]

Returns True if the input src is of type torch.sparse.Tensor (in any sparse layout) or of type torch_sparse.SparseTensor.

Parameters:

src (Any) – The input object to be checked.

to_torch_coo_tensor(edge_index: Tensor, edge_attr: = None, size: Optional[Union[int, Tuple[Optional[int], Optional[int]]]] = None, is_coalesced: bool = False) [source]

Converts a sparse adjacency matrix defined by edge indices and edge attributes to a torch.sparse.Tensor with layout torch.sparse_coo. See to_edge_index() for the reverse operation.

Parameters:
• edge_index (LongTensor) – The edge indices.

• edge_attr (Tensor, optional) – The edge attributes. (default: None)

• size (int or (int, int), optional) – The size of the sparse matrix. If given as an integer, will create a quadratic sparse matrix. If set to None, will infer a quadratic sparse matrix based on edge_index.max() + 1. (default: None)

• is_coalesced (bool) – If set to True, will assume that edge_index is already coalesced and thus avoids expensive computation. (default: False)

Return type:

torch.sparse.Tensor

Example

>>> edge_index = torch.tensor([[0, 1, 1, 2, 2, 3],
...                            [1, 0, 2, 1, 3, 2]])
>>> to_torch_coo_tensor(edge_index)
tensor(indices=tensor([[0, 1, 1, 2, 2, 3],
[1, 0, 2, 1, 3, 2]]),
values=tensor([1., 1., 1., 1., 1., 1.]),
size=(4, 4), nnz=6, layout=torch.sparse_coo)
to_torch_csr_tensor(edge_index: Tensor, edge_attr: = None, size: Optional[Union[int, Tuple[Optional[int], Optional[int]]]] = None, is_coalesced: bool = False) [source]

Converts a sparse adjacency matrix defined by edge indices and edge attributes to a torch.sparse.Tensor with layout torch.sparse_csr. See to_edge_index() for the reverse operation.

Parameters:
• edge_index (LongTensor) – The edge indices.

• edge_attr (Tensor, optional) – The edge attributes. (default: None)

• size (int or (int, int), optional) – The size of the sparse matrix. If given as an integer, will create a quadratic sparse matrix. If set to None, will infer a quadratic sparse matrix based on edge_index.max() + 1. (default: None)

• is_coalesced (bool) – If set to True, will assume that edge_index is already coalesced and thus avoids expensive computation. (default: False)

Return type:

torch.sparse.Tensor

Example

>>> edge_index = torch.tensor([[0, 1, 1, 2, 2, 3],
...                            [1, 0, 2, 1, 3, 2]])
>>> to_torch_csr_tensor(edge_index)
tensor(crow_indices=tensor([0, 1, 3, 5, 6]),
col_indices=tensor([1, 0, 2, 1, 3, 2]),
values=tensor([1., 1., 1., 1., 1., 1.]),
size=(4, 4), nnz=6, layout=torch.sparse_csr)
to_torch_csc_tensor(edge_index: Tensor, edge_attr: = None, size: Optional[Union[int, Tuple[Optional[int], Optional[int]]]] = None, is_coalesced: bool = False) [source]

Converts a sparse adjacency matrix defined by edge indices and edge attributes to a torch.sparse.Tensor with layout torch.sparse_csc. See to_edge_index() for the reverse operation.

Parameters:
• edge_index (LongTensor) – The edge indices.

• edge_attr (Tensor, optional) – The edge attributes. (default: None)

• size (int or (int, int), optional) – The size of the sparse matrix. If given as an integer, will create a quadratic sparse matrix. If set to None, will infer a quadratic sparse matrix based on edge_index.max() + 1. (default: None)

• is_coalesced (bool) – If set to True, will assume that edge_index is already coalesced and thus avoids expensive computation. (default: False)

Return type:

torch.sparse.Tensor

Example

>>> edge_index = torch.tensor([[0, 1, 1, 2, 2, 3],
...                            [1, 0, 2, 1, 3, 2]])
>>> to_torch_csc_tensor(edge_index)
tensor(ccol_indices=tensor([0, 1, 3, 5, 6]),
row_indices=tensor([1, 0, 2, 1, 3, 2]),
values=tensor([1., 1., 1., 1., 1., 1.]),
size=(4, 4), nnz=6, layout=torch.sparse_csc)
to_torch_sparse_tensor(edge_index: Tensor, edge_attr: = None, size: Optional[Union[int, Tuple[Optional[int], Optional[int]]]] = None, is_coalesced: bool = False, layout: layout = torch.sparse_coo) [source]

Converts a sparse adjacency matrix defined by edge indices and edge attributes to a torch.sparse.Tensor with custom layout. See to_edge_index() for the reverse operation.

Parameters:
• edge_index (LongTensor) – The edge indices.

• edge_attr (Tensor, optional) – The edge attributes. (default: None)

• size (int or (int, int), optional) – The size of the sparse matrix. If given as an integer, will create a quadratic sparse matrix. If set to None, will infer a quadratic sparse matrix based on edge_index.max() + 1. (default: None)

• is_coalesced (bool) – If set to True, will assume that edge_index is already coalesced and thus avoids expensive computation. (default: False)

• layout (torch.layout, optional) – The layout of the output sparse tensor (torch.sparse_coo, torch.sparse_csr, torch.sparse_csc). (default: torch.sparse_coo)

Return type:

torch.sparse.Tensor

Converts a torch.sparse.Tensor or a torch_sparse.SparseTensor to edge indices and edge attributes.

Parameters:

Return type:

Example

>>> edge_index = torch.tensor([[0, 1, 1, 2, 2, 3],
...                            [1, 0, 2, 1, 3, 2]])
(tensor([[0, 1, 1, 2, 2, 3],
[1, 0, 2, 1, 3, 2]]),
tensor([1., 1., 1., 1., 1., 1.]))
spmm(src: Union[Tensor, SparseTensor], other: Tensor, reduce: str = 'sum') [source]

Matrix product of sparse matrix with dense matrix.

Parameters:
• src (torch.Tensor or torch_sparse.SparseTensor) – The input sparse matrix, either a torch_sparse.SparseTensor or a torch.sparse.Tensor.

• other (torch.Tensor) – The input dense matrix.

• reduce (str, optional) – The reduce operation to use ("sum", "mean", "min", "max"). (default: "sum")

Return type:

Tensor

unbatch(src: Tensor, batch: Tensor, dim: int = 0, batch_size: = None) [source]

Splits src according to a batch vector along dimension dim.

Parameters:
• src (Tensor) – The source tensor.

• batch (LongTensor) – The batch vector $$\mathbf{b} \in {\{ 0, \ldots, B-1\}}^N$$, which assigns each entry in src to a specific example. Must be ordered.

• dim (int, optional) – The dimension along which to split the src tensor. (default: 0)

• batch_size (int, optional) – The batch size. (default: None)

Return type:

List[Tensor]

Example

>>> src = torch.arange(7)
>>> batch = torch.tensor([0, 0, 0, 1, 1, 2, 2])
>>> unbatch(src, batch)
(tensor([0, 1, 2]), tensor([3, 4]), tensor([5, 6]))
unbatch_edge_index(edge_index: Tensor, batch: Tensor, batch_size: = None) [source]

Splits the edge_index according to a batch vector.

Parameters:
• edge_index (Tensor) – The edge_index tensor. Must be ordered.

• batch (LongTensor) – The batch vector $$\mathbf{b} \in {\{ 0, \ldots, B-1\}}^N$$, which assigns each node to a specific example. Must be ordered.

• batch_size (int, optional) – The batch size. (default: None)

Return type:

List[Tensor]

Example

>>> edge_index = torch.tensor([[0, 1, 1, 2, 2, 3, 4, 5, 5, 6],
...                            [1, 0, 2, 1, 3, 2, 5, 4, 6, 5]])
>>> batch = torch.tensor([0, 0, 0, 0, 1, 1, 1])
>>> unbatch_edge_index(edge_index, batch)
(tensor([[0, 1, 1, 2, 2, 3],
[1, 0, 2, 1, 3, 2]]),
tensor([[0, 1, 1, 2],
[1, 0, 2, 1]]))
one_hot(index: Tensor, num_classes: = None, dtype: = None) [source]

Taskes a one-dimensional index tensor and returns a one-hot encoded representation of it with shape [*, num_classes] that has zeros everywhere except where the index of last dimension matches the corresponding value of the input tensor, in which case it will be 1.

Note

This is a more memory-efficient version of torch.nn.functional.one_hot() as you can customize the output dtype.

Parameters:
• index (torch.Tensor) – The one-dimensional input tensor.

• num_classes (int, optional) – The total number of classes. If set to None, the number of classes will be inferred as one greater than the largest class value in the input tensor. (default: None)

• dtype (torch.dtype, optional) – The dtype of the output tensor.

normalized_cut(edge_index: Tensor, edge_attr: Tensor, num_nodes: = None) [source]

Computes the normalized cut $$\mathbf{e}_{i,j} \cdot \left( \frac{1}{\deg(i)} + \frac{1}{\deg(j)} \right)$$ of a weighted graph given by edge indices and edge attributes.

Parameters:
• edge_index (LongTensor) – The edge indices.

• edge_attr (Tensor) – Edge weights or multi-dimensional edge features.

• num_nodes (int, optional) – The number of nodes, i.e. max_val + 1 of edge_index. (default: None)

Return type:

Tensor

Example

>>> edge_index = torch.tensor([[1, 1, 2, 3],
...                            [3, 3, 1, 2]])
>>> edge_attr = torch.tensor([1., 1., 1., 1.])
>>> normalized_cut(edge_index, edge_attr)
tensor([1.5000, 1.5000, 2.0000, 1.5000])
grid(height: int, width: int, dtype: = None, device: = None) [source]

Returns the edge indices of a two-dimensional grid graph with height height and width width and its node positions.

Parameters:
• height (int) – The height of the grid.

• width (int) – The width of the grid.

• dtype (torch.dtype, optional) – The desired data type of the returned position tensor. (default: None)

• device (torch.device, optional) – The desired device of the returned tensors. (default: None)

Return type:

(LongTensor, Tensor)

Example

>>> (row, col), pos = grid(height=2, width=2)
>>> row
tensor([0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3])
>>> col
tensor([0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3])
>>> pos
tensor([[0., 1.],
[1., 1.],
[0., 0.],
[1., 0.]])
geodesic_distance(pos: Tensor, face: Tensor, src: = None, dst: = None, norm: bool = True, max_distance: = None, num_workers: int = 0, **kwargs: ) [source]

Computes (normalized) geodesic distances of a mesh given by pos and face. If src and dst are given, this method only computes the geodesic distances for the respective source and target node-pairs.

Note

This function requires the gdist package. To install, run pip install cython && pip install gdist.

Parameters:
• pos (torch.Tensor) – The node positions.

• face (torch.Tensor) – The face indices.

• src (torch.Tensor, optional) – If given, only compute geodesic distances for the specified source indices. (default: None)

• dst (torch.Tensor, optional) – If given, only compute geodesic distances for the specified target indices. (default: None)

• norm (bool, optional) – Normalizes geodesic distances by $$\sqrt{\textrm{area}(\mathcal{M})}$$. (default: True)

• max_distance (float, optional) – If given, only yields results for geodesic distances less than max_distance. This will speed up runtime dramatically. (default: None)

• num_workers (int, optional) – How many subprocesses to use for calculating geodesic distances. 0 means that computation takes place in the main process. -1 means that the available amount of CPU cores is used. (default: 0)

Return type:

Tensor

Example

>>> pos = torch.tensor([[0.0, 0.0, 0.0],
...                     [2.0, 0.0, 0.0],
...                     [0.0, 2.0, 0.0],
...                     [2.0, 2.0, 0.0]])
>>> face = torch.tensor([[0, 0],
...                      [1, 2],
...                      [3, 3]])
>>> geodesic_distance(pos, face)
[[0, 1, 1, 1.4142135623730951],
[1, 0, 1.4142135623730951, 1],
[1, 1.4142135623730951, 0, 1],
[1.4142135623730951, 1, 1, 0]]
to_scipy_sparse_matrix(edge_index: Tensor, edge_attr: = None, num_nodes: = None) coo_matrix[source]

Converts a graph given by edge indices and edge attributes to a scipy sparse matrix.

Parameters:
• edge_index (LongTensor) – The edge indices.

• edge_attr (Tensor, optional) – Edge weights or multi-dimensional edge features. (default: None)

• num_nodes (int, optional) – The number of nodes, i.e. max_val + 1 of index. (default: None)

Examples

>>> edge_index = torch.tensor([
...     [0, 1, 1, 2, 2, 3],
...     [1, 0, 2, 1, 3, 2],
... ])
>>> to_scipy_sparse_matrix(edge_index)
<4x4 sparse matrix of type '<class 'numpy.float32'>'
with 6 stored elements in COOrdinate format>
from_scipy_sparse_matrix(A: spmatrix) [source]

Converts a scipy sparse matrix to edge indices and edge attributes.

Parameters:

A (scipy.sparse) – A sparse matrix.

Examples

>>> edge_index = torch.tensor([
...     [0, 1, 1, 2, 2, 3],
...     [1, 0, 2, 1, 3, 2],
... ])
>>> # edge_index and edge_weight are both returned
(tensor([[0, 1, 1, 2, 2, 3],
[1, 0, 2, 1, 3, 2]]),
tensor([1., 1., 1., 1., 1., 1.]))
to_networkx(data: , node_attrs: = None, edge_attrs: = None, graph_attrs: = None, to_undirected: Optional[Union[bool, str]] = False, to_multi: bool = False, remove_self_loops: bool = False) Any[source]

Converts a torch_geometric.data.Data instance to a networkx.Graph if to_undirected is set to True, or a directed networkx.DiGraph otherwise.

Parameters:
• data (torch_geometric.data.Data or torch_geometric.data.HeteroData) – A homogeneous or heterogeneous data object.

• node_attrs (iterable of str, optional) – The node attributes to be copied. (default: None)

• edge_attrs (iterable of str, optional) – The edge attributes to be copied. (default: None)

• graph_attrs (iterable of str, optional) – The graph attributes to be copied. (default: None)

• to_undirected (bool or str, optional) – If set to True, will return a networkx.Graph instead of a networkx.DiGraph. By default, will include all edges and make them undirected. If set to "upper", the undirected graph will only correspond to the upper triangle of the input adjacency matrix. If set to "lower", the undirected graph will only correspond to the lower triangle of the input adjacency matrix. Only applicable in case the data object holds a homogeneous graph. (default: False)

• to_multi (bool, optional) – if set to True, will return a networkx.MultiGraph or a networkx:MultiDiGraph (depending on the to_undirected option), which will not drop duplicated edges that may exist in data. (default: False)

• remove_self_loops (bool, optional) – If set to True, will not include self-loops in the resulting graph. (default: False)

Examples

>>> edge_index = torch.tensor([
...     [0, 1, 1, 2, 2, 3],
...     [1, 0, 2, 1, 3, 2],
... ])
>>> data = Data(edge_index=edge_index, num_nodes=4)
>>> to_networkx(data)
<networkx.classes.digraph.DiGraph at 0x2713fdb40d0>
from_networkx(G: Any, group_node_attrs: Optional[Union[List[str], Literal['all']]] = None, group_edge_attrs: Optional[Union[List[str], Literal['all']]] = None) Data[source]

Converts a networkx.Graph or networkx.DiGraph to a torch_geometric.data.Data instance.

Parameters:
• G (networkx.Graph or networkx.DiGraph) – A networkx graph.

• group_node_attrs (List[str] or "all", optional) – The node attributes to be concatenated and added to data.x. (default: None)

• group_edge_attrs (List[str] or "all", optional) – The edge attributes to be concatenated and added to data.edge_attr. (default: None)

Note

All group_node_attrs and group_edge_attrs values must be numeric.

Examples

>>> edge_index = torch.tensor([
...     [0, 1, 1, 2, 2, 3],
...     [1, 0, 2, 1, 3, 2],
... ])
>>> data = Data(edge_index=edge_index, num_nodes=4)
>>> g = to_networkx(data)
>>> # A Data object is returned
>>> from_networkx(g)
Data(edge_index=[2, 6], num_nodes=4)
to_networkit(edge_index: Tensor, edge_weight: = None, num_nodes: = None, directed: bool = True) Any[source]

Converts a (edge_index, edge_weight) tuple to a networkit.Graph.

Parameters:
• edge_index (torch.Tensor) – The edge indices of the graph.

• edge_weight (torch.Tensor, optional) – The edge weights of the graph. (default: None)

• num_nodes (int, optional) – The number of nodes in the graph. (default: None)

• directed (bool, optional) – If set to False, the graph will be undirected. (default: True)

from_networkit(g: Any) [source]

Converts a networkit.Graph to a (edge_index, edge_weight) tuple. If the networkit.Graph is not weighted, the returned edge_weight will be None.

Parameters:

g (networkkit.graph.Graph) – A networkit graph object.

to_trimesh(data: Data) Any[source]

Converts a torch_geometric.data.Data instance to a trimesh.Trimesh.

Parameters:

data (torch_geometric.data.Data) – The data object.

Example

>>> pos = torch.tensor([[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0]],
...                    dtype=torch.float)
>>> face = torch.tensor([[0, 1, 2], [1, 2, 3]]).t()
>>> data = Data(pos=pos, face=face)
>>> to_trimesh(data)
<trimesh.Trimesh(vertices.shape=(4, 3), faces.shape=(2, 3))>
from_trimesh(mesh: Any) Data[source]

Converts a trimesh.Trimesh to a torch_geometric.data.Data instance.

Parameters:

mesh (trimesh.Trimesh) – A trimesh mesh.

Example

>>> pos = torch.tensor([[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0]],
...                    dtype=torch.float)
>>> face = torch.tensor([[0, 1, 2], [1, 2, 3]]).t()
>>> data = Data(pos=pos, face=face)
>>> mesh = to_trimesh(data)
>>> from_trimesh(mesh)
Data(pos=[4, 3], face=[3, 2])
to_cugraph(edge_index: Tensor, edge_weight: = None, relabel_nodes: bool = True, directed: bool = True) Any[source]

Converts a graph given by edge_index and optional edge_weight into a cugraph graph object.

Parameters:
• edge_index (torch.Tensor) – The edge indices of the graph.

• edge_weight (torch.Tensor, optional) – The edge weights of the graph. (default: None)

• relabel_nodes (bool, optional) – If set to True, cugraph will remove any isolated nodes, leading to a relabeling of nodes. (default: True)

• directed (bool, optional) – If set to False, the graph will be undirected. (default: True)

from_cugraph(g: Any) [source]

Converts a cugraph graph object into edge_index and optional edge_weight tensors.

Parameters:

g (cugraph.Graph) – A cugraph graph object.

to_dgl(data: ) Any[source]

Converts a torch_geometric.data.Data or torch_geometric.data.HeteroData instance to a dgl graph object.

Parameters:

data (torch_geometric.data.Data or torch_geometric.data.HeteroData) – The data object.

Example

>>> edge_index = torch.tensor([[0, 1, 1, 2, 3, 0], [1, 0, 2, 1, 4, 4]])
>>> x = torch.randn(5, 3)
>>> edge_attr = torch.randn(6, 2)
>>> data = Data(x=x, edge_index=edge_index, edge_attr=y)
>>> g = to_dgl(data)
>>> g
Graph(num_nodes=5, num_edges=6,
ndata_schemes={'x': Scheme(shape=(3,))}
edata_schemes={'edge_attr': Scheme(shape=(2, ))})
>>> data = HeteroData()
>>> data['paper'].x = torch.randn(5, 3)
>>> data['author'].x = torch.ones(5, 3)
>>> edge_index = torch.tensor([[0, 1, 2, 3, 4], [0, 1, 2, 3, 4]])
>>> data['author', 'cites', 'paper'].edge_index = edge_index
>>> g = to_dgl(data)
>>> g
Graph(num_nodes={'author': 5, 'paper': 5},
num_edges={('author', 'cites', 'paper'): 5},
metagraph=[('author', 'paper', 'cites')])
from_dgl(g: Any) [source]

Converts a dgl graph object to a torch_geometric.data.Data or torch_geometric.data.HeteroData instance.

Parameters:

g (dgl.DGLGraph) – The dgl graph object.

Example

>>> g = dgl.graph(([0, 0, 1, 5], [1, 2, 2, 0]))
>>> g.ndata['x'] = torch.randn(g.num_nodes(), 3)
>>> g.edata['edge_attr'] = torch.randn(g.num_edges(), 2)
>>> data = from_dgl(g)
>>> data
Data(x=[6, 3], edge_attr=[4, 2], edge_index=[2, 4])
>>> g = dgl.heterograph({
>>> g = dgl.heterograph({
...     ('author', 'writes', 'paper'): ([0, 1, 1, 2, 3, 3, 4],
...                                     [0, 0, 1, 1, 1, 2, 2])})
>>> g.nodes['author'].data['x'] = torch.randn(5, 3)
>>> g.nodes['paper'].data['x'] = torch.randn(5, 3)
>>> data = from_dgl(g)
>>> data
HeteroData(
author={ x=[5, 3] },
paper={ x=[3, 3] },
(author, writes, paper)={ edge_index=[2, 7] }
)
from_smiles(smiles: str, with_hydrogen: bool = False, kekulize: bool = False) Data[source]

Converts a SMILES string to a torch_geometric.data.Data instance.

Parameters:
• smiles (str) – The SMILES string.

• with_hydrogen (bool, optional) – If set to True, will store hydrogens in the molecule graph. (default: False)

• kekulize (bool, optional) – If set to True, converts aromatic bonds to single/double bonds. (default: False)

to_smiles(data: Data, kekulize: bool = False) Any[source]

Converts a torch_geometric.data.Data instance to a SMILES string.

Parameters:
erdos_renyi_graph(num_nodes: int, edge_prob: float, directed: bool = False) [source]

Returns the edge_index of a random Erdos-Renyi graph.

Parameters:
• num_nodes (int) – The number of nodes.

• edge_prob (float) – Probability of an edge.

• directed (bool, optional) – If set to True, will return a directed graph. (default: False)

Examples

>>> erdos_renyi_graph(5, 0.2, directed=False)
tensor([[0, 1, 1, 4],
[1, 0, 4, 1]])
>>> erdos_renyi_graph(5, 0.2, directed=True)
tensor([[0, 1, 3, 3, 4, 4],
[4, 3, 1, 2, 1, 3]])
stochastic_blockmodel_graph(block_sizes: Union[List[int], Tensor], edge_probs: Union[List[List[float]], Tensor], directed: bool = False) [source]

Returns the edge_index of a stochastic blockmodel graph.

Parameters:
• block_sizes ([int] or LongTensor) – The sizes of blocks.

• edge_probs ([[float]] or FloatTensor) – The density of edges going from each block to each other block. Must be symmetric if the graph is undirected.

• directed (bool, optional) – If set to True, will return a directed graph. (default: False)

Examples

>>> block_sizes = [2, 2, 4]
>>> edge_probs = [[0.25, 0.05, 0.02],
...               [0.05, 0.35, 0.07],
...               [0.02, 0.07, 0.40]]
>>> stochastic_blockmodel_graph(block_sizes, edge_probs,
...                             directed=False)
tensor([[2, 4, 4, 5, 5, 6, 7, 7],
[5, 6, 7, 2, 7, 4, 4, 5]])
>>> stochastic_blockmodel_graph(block_sizes, edge_probs,
...                             directed=True)
tensor([[0, 2, 3, 4, 4, 5, 5],
[3, 4, 1, 5, 6, 6, 7]])
barabasi_albert_graph(num_nodes: int, num_edges: int) [source]

Returns the edge_index of a Barabasi-Albert preferential attachment model, where a graph of num_nodes nodes grows by attaching new nodes with num_edges edges that are preferentially attached to existing nodes with high degree.

Parameters:
• num_nodes (int) – The number of nodes.

• num_edges (int) – The number of edges from a new node to existing nodes.

Example

>>> barabasi_albert_graph(num_nodes=4, num_edges=3)
tensor([[0, 0, 0, 1, 1, 2, 2, 3],
[1, 2, 3, 0, 2, 0, 1, 0]])
negative_sampling(edge_index: Tensor, num_nodes: Optional[Union[int, Tuple[int, int]]] = None, num_neg_samples: = None, method: str = 'sparse', force_undirected: bool = False) [source]

Samples random negative edges of a graph given by edge_index.

Parameters:
• edge_index (LongTensor) – The edge indices.

• num_nodes (int or Tuple[int, int], optional) – The number of nodes, i.e. max_val + 1 of edge_index. If given as a tuple, then edge_index is interpreted as a bipartite graph with shape (num_src_nodes, num_dst_nodes). (default: None)

• num_neg_samples (int, optional) – The (approximate) number of negative samples to return. If set to None, will try to return a negative edge for every positive edge. (default: None)

• method (str, optional) – The method to use for negative sampling, i.e. "sparse" or "dense". This is a memory/runtime trade-off. "sparse" will work on any graph of any size, while "dense" can perform faster true-negative checks. (default: "sparse")

• force_undirected (bool, optional) – If set to True, sampled negative edges will be undirected. (default: False)

Return type:

LongTensor

Examples

>>> # Standard usage
>>> edge_index = torch.as_tensor([[0, 0, 1, 2],
...                               [0, 1, 2, 3]])
>>> negative_sampling(edge_index)
tensor([[3, 0, 0, 3],
[2, 3, 2, 1]])
>>> # For bipartite graph
>>> negative_sampling(edge_index, num_nodes=(3, 4))
tensor([[0, 2, 2, 1],
[2, 2, 1, 3]])
batched_negative_sampling(edge_index: Tensor, batch: , num_neg_samples: = None, method: str = 'sparse', force_undirected: bool = False) [source]

Samples random negative edges of multiple graphs given by edge_index and batch.

Parameters:
• edge_index (LongTensor) – The edge indices.

• batch (LongTensor or Tuple[LongTensor, LongTensor]) – Batch vector $$\mathbf{b} \in {\{ 0, \ldots, B-1\}}^N$$, which assigns each node to a specific example. If given as a tuple, then edge_index is interpreted as a bipartite graph connecting two different node types.

• num_neg_samples (int, optional) – The number of negative samples to return. If set to None, will try to return a negative edge for every positive edge. (default: None)

• method (str, optional) – The method to use for negative sampling, i.e. "sparse" or "dense". This is a memory/runtime trade-off. "sparse" will work on any graph of any size, while "dense" can perform faster true-negative checks. (default: "sparse")

• force_undirected (bool, optional) – If set to True, sampled negative edges will be undirected. (default: False)

Return type:

LongTensor

Examples

>>> # Standard usage
>>> edge_index = torch.as_tensor([[0, 0, 1, 2], [0, 1, 2, 3]])
>>> edge_index = torch.cat([edge_index, edge_index + 4], dim=1)
>>> edge_index
tensor([[0, 0, 1, 2, 4, 4, 5, 6],
[0, 1, 2, 3, 4, 5, 6, 7]])
>>> batch = torch.tensor([0, 0, 0, 0, 1, 1, 1, 1])
>>> batched_negative_sampling(edge_index, batch)
tensor([[3, 1, 3, 2, 7, 7, 6, 5],
[2, 0, 1, 1, 5, 6, 4, 4]])
>>> # For bipartite graph
>>> edge_index1 = torch.as_tensor([[0, 0, 1, 1], [0, 1, 2, 3]])
>>> edge_index2 = edge_index1 + torch.tensor([[2], [4]])
>>> edge_index3 = edge_index2 + torch.tensor([[2], [4]])
>>> edge_index = torch.cat([edge_index1, edge_index2,
...                         edge_index3], dim=1)
>>> edge_index
tensor([[ 0,  0,  1,  1,  2,  2,  3,  3,  4,  4,  5,  5],
[ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11]])
>>> src_batch = torch.tensor([0, 0, 1, 1, 2, 2])
>>> dst_batch = torch.tensor([0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2])
>>> batched_negative_sampling(edge_index,
...                           (src_batch, dst_batch))
tensor([[ 0,  0,  1,  1,  2,  2,  3,  3,  4,  4,  5,  5],
[ 2,  3,  0,  1,  6,  7,  4,  5, 10, 11,  8,  9]])
structured_negative_sampling(edge_index: Tensor, num_nodes: = None, contains_neg_self_loops: bool = True) [source]

Samples a negative edge (i,k) for every positive edge (i,j) in the graph given by edge_index, and returns it as a tuple of the form (i,j,k).

Parameters:
• edge_index (LongTensor) – The edge indices.

• num_nodes (int, optional) – The number of nodes, i.e. max_val + 1 of edge_index. (default: None)

• contains_neg_self_loops (bool, optional) – If set to False, sampled negative edges will not contain self loops. (default: True)

Return type:

(LongTensor, LongTensor, LongTensor)

Example

>>> edge_index = torch.as_tensor([[0, 0, 1, 2],
...                               [0, 1, 2, 3]])
>>> structured_negative_sampling(edge_index)
(tensor([0, 0, 1, 2]), tensor([0, 1, 2, 3]), tensor([2, 3, 0, 2]))
structured_negative_sampling_feasible(edge_index: Tensor, num_nodes: = None, contains_neg_self_loops: bool = True) bool[source]

Returns True if structured_negative_sampling() is feasible on the graph given by edge_index. structured_negative_sampling() is infeasible if atleast one node is connected to all other nodes.

Parameters:
• edge_index (LongTensor) – The edge indices.

• num_nodes (int, optional) – The number of nodes, i.e. max_val + 1 of edge_index. (default: None)

• contains_neg_self_loops (bool, optional) – If set to False, sampled negative edges will not contain self loops. (default: True)

Return type:

bool

Examples

>>> edge_index = torch.LongTensor([[0, 0, 1, 1, 2, 2, 2],
...                                [1, 2, 0, 2, 0, 1, 1]])
>>> structured_negative_sampling_feasible(edge_index, 3, False)
False
>>> structured_negative_sampling_feasible(edge_index, 3, True)
True
shuffle_node(x: Tensor, batch: = None, training: bool = True) [source]

Randomly shuffle the feature matrix x along the first dimmension.

The method returns (1) the shuffled x, (2) the permutation indicating the orders of original nodes after shuffling.

Parameters:
• x (FloatTensor) – The feature matrix.

• batch (LongTensor, optional) – Batch vector $$\mathbf{b} \in {\{ 0, \ldots, B-1\}}^N$$, which assigns each node to a specific example. Must be ordered. (default: None)

• training (bool, optional) – If set to False, this operation is a no-op. (default: True)

Return type:

(FloatTensor, LongTensor)

Example

>>> # Standard case
>>> x = torch.tensor([[0, 1, 2],
...                   [3, 4, 5],
...                   [6, 7, 8],
...                   [9, 10, 11]], dtype=torch.float)
>>> x, node_perm = shuffle_node(x)
>>> x
tensor([[ 3.,  4.,  5.],
[ 9., 10., 11.],
[ 0.,  1.,  2.],
[ 6.,  7.,  8.]])
>>> node_perm
tensor([1, 3, 0, 2])
>>> # For batched graphs as inputs
>>> batch = torch.tensor([0, 0, 1, 1])
>>> x, node_perm = shuffle_node(x, batch)
>>> x
tensor([[ 3.,  4.,  5.],
[ 0.,  1.,  2.],
[ 9., 10., 11.],
[ 6.,  7.,  8.]])
>>> node_perm
tensor([1, 0, 3, 2])
mask_feature(x: Tensor, p: float = 0.5, mode: str = 'col', fill_value: float = 0.0, training: bool = True) [source]

Randomly masks feature from the feature matrix x with probability p using samples from a Bernoulli distribution.

The method returns (1) the retained x, (2) the feature mask broadcastable with x (mode='row' and mode='col') or with the same shape as x (mode='all'), indicating where features are retained.

Parameters:
• x (FloatTensor) – The feature matrix.

• p (float, optional) – The masking ratio. (default: 0.5)

• mode (str, optional) – The masked scheme to use for feature masking. ("row", "col" or "all"). If mode='col', will mask entire features of all nodes from the feature matrix. If mode='row', will mask entire nodes from the feature matrix. If mode='all', will mask individual features across all nodes. (default: 'col')

• fill_value (float, optional) – The value for masked features in the output tensor. (default: 0)

• training (bool, optional) – If set to False, this operation is a no-op. (default: True)

Return type:

(FloatTensor, BoolTensor)

Examples

>>> # Masked features are column-wise sampled
>>> x = torch.tensor([[1, 2, 3],
...                   [4, 5, 6],
...                   [7, 8, 9]], dtype=torch.float)
>>> x
tensor([[1., 0., 3.],
[4., 0., 6.],
[7., 0., 9.]]),
tensor([[True, False, True]])
>>> # Masked features are row-wise sampled
>>> x
tensor([[1., 2., 3.],
[0., 0., 0.],
[7., 8., 9.]]),
tensor([[True], [False], [True]])
>>> # Masked features are uniformly sampled
>>> x
tensor([[0., 0., 0.],
[4., 0., 6.],
[0., 0., 9.]])
tensor([[False, False, False],
[True, False,  True],
[False, False,  True]])
add_random_edge(edge_index: Tensor, p: float = 0.5, force_undirected: bool = False, num_nodes: Optional[Union[int, Tuple[int, int]]] = None, training: bool = True) [source]

The method returns (1) the retained edge_index, (2) the added edge indices.

Parameters:
• edge_index (LongTensor) – The edge indices.

• p (float) – Ratio of added edges to the existing edges. (default: 0.5)

• force_undirected (bool, optional) – If set to True, added edges will be undirected. (default: False)

• num_nodes (int, Tuple[int], optional) – The overall number of nodes, i.e. max_val + 1, or the number of source and destination nodes, i.e. (max_src_val + 1, max_dst_val + 1) of edge_index. (default: None)

• training (bool, optional) – If set to False, this operation is a no-op. (default: True)

Return type:

(LongTensor, LongTensor)

Examples

>>> # Standard case
>>> edge_index = torch.tensor([[0, 1, 1, 2, 2, 3],
...                            [1, 0, 2, 1, 3, 2]])
>>> edge_index
tensor([[0, 1, 1, 2, 2, 3, 2, 1, 3],
[1, 0, 2, 1, 3, 2, 0, 2, 1]])
tensor([[2, 1, 3],
[0, 2, 1]])
>>> # The returned graph is kept undirected
...                                           force_undirected=True)
>>> edge_index
tensor([[0, 1, 1, 2, 2, 3, 2, 1, 3, 0, 2, 1],
[1, 0, 2, 1, 3, 2, 0, 2, 1, 2, 1, 3]])
tensor([[2, 1, 3, 0, 2, 1],
[0, 2, 1, 2, 1, 3]])
>>> # For bipartite graphs
>>> edge_index = torch.tensor([[0, 1, 2, 3, 4, 5],
...                            [2, 3, 1, 4, 2, 1]])
...                                           num_nodes=(6, 5))
>>> edge_index
tensor([[0, 1, 2, 3, 4, 5, 3, 4, 1],
[2, 3, 1, 4, 2, 1, 1, 3, 2]])
tensor([[3, 4, 1],
[1, 3, 2]])
tree_decomposition(mol: Any, return_vocab: bool = False) [source]

The tree decomposition algorithm of molecules from the “Junction Tree Variational Autoencoder for Molecular Graph Generation” paper. Returns the graph connectivity of the junction tree, the assignment mapping of each atom to the clique in the junction tree, and the number of cliques.

Parameters:
• mol (rdkit.Chem.Mol) – An rdkit molecule.

• return_vocab (bool, optional) – If set to True, will return an identifier for each clique (ring, bond, bridged compounds, single). (default: False)

Return type:

(LongTensor, LongTensor, int) if return_vocab is False, else (LongTensor, LongTensor, int, LongTensor)

get_embeddings(model: Module, *args: Any, **kwargs: Any) [source]

Returns the output embeddings of all MessagePassing layers in model.

Internally, this method registers forward hooks on all MessagePassing layers of a model, and runs the forward pass of the model by calling model(*args, **kwargs).

Parameters:
• model (torch.nn.Module) – The message passing model.

• *args – Arguments passed to the model.

• **kwargs (optional) – Additional keyword arguments passed to the model.

trim_to_layer(layer: int, num_sampled_nodes_per_hop: Union[List[int], Dict[str, List[int]]], num_sampled_edges_per_hop: Union[List[int], Dict[Tuple[str, str, str], List[int]]], x: Union[Tensor, Dict[str, Tensor]], edge_index: Union[Tensor, Dict[Tuple[str, str, str], Tensor]], edge_attr: Optional[Union[Tensor, Dict[Tuple[str, str, str], Tensor]]] = None) Tuple[Union[Tensor, Dict[str, Tensor]], Union[Tensor, Dict[Tuple[str, str, str], Union[Tensor, SparseTensor]]], Optional[Union[Tensor, Dict[Tuple[str, str, str], Tensor]]]][source]

Trims the edge_index representation, node features x and edge features edge_attr to a minimal-sized representation for the current GNN layer layer in directed NeighborLoader scenarios.

This ensures that no computation is performed for nodes and edges that are not included in the current GNN layer, thus avoiding unnecessary computation within the GNN when performing neighborhood sampling.

Parameters:
• layer (int) – The current GNN layer.

• num_sampled_nodes_per_hop (List[int] or Dict[NodeType, List[int]]) – The number of sampled nodes per hop.

• num_sampled_edges_per_hop (List[int] or Dict[EdgeType, List[int]]) – The number of sampled edges per hop.

• x (torch.Tensor or Dict[NodeType, torch.Tensor]) – The homogeneous or heterogeneous (hidden) node features.

• edge_index (torch.Tensor or Dict[EdgeType, torch.Tensor]) – The homogeneous or heterogeneous edge indices.

• edge_attr (torch.Tensor or Dict[EdgeType, torch.Tensor], optional) – The homogeneous or heterogeneous (hidden) edge features.

get_ppr(edge_index: Tensor, alpha: float = 0.2, eps: float = 1e-05, target: = None, num_nodes: = None) [source]

Calculates the personalized PageRank (PPR) vector for all or a subset of nodes using a variant of the Andersen algorithm.

Parameters:
• edge_index (torch.Tensor) – The indices of the graph.

• alpha (float, optional) – The alpha value of the PageRank algorithm. (default: 0.2)

• eps (float, optional) – The threshold for stopping the PPR calculation (edge_weight >= eps * out_degree). (default: 1e-5)

• target (torch.Tensor, optional) – The target nodes to compute PPR for. If not given, calculates PPR vectors for all nodes. (default: None)

• num_nodes (int, optional) – The number of nodes. (default: None)

Return type:
train_test_split_edges(data: Data, val_ratio: float = 0.05, test_ratio: float = 0.1) Data[source]

Splits the edges of a torch_geometric.data.Data object into positive and negative train/val/test edges. As such, it will replace the edge_index attribute with train_pos_edge_index, train_pos_neg_adj_mask, val_pos_edge_index, val_neg_edge_index and test_pos_edge_index attributes. If data has edge features named edge_attr, then train_pos_edge_attr, val_pos_edge_attr and test_pos_edge_attr will be added as well.

Warning

train_test_split_edges() is deprecated and will be removed in a future release. Use torch_geometric.transforms.RandomLinkSplit instead.

Parameters:
• data (Data) – The data object.

• val_ratio (float, optional) – The ratio of positive validation edges. (default: 0.05)

• test_ratio (float, optional) – The ratio of positive test edges. (default: 0.1)

Return type:

torch_geometric.data.Data