torch_geometric.utils

scatter	Reduces all values from the src tensor at the indices specified in the index tensor along a given dimension dim.
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.
degree	Computes the (unweighted) degree of a given one-dimensional index tensor.
softmax	Computes a sparsely evaluated softmax.
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.
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.
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.
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_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
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.
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).
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.
train_test_split_edges	Splits the edges of a torch_geometric.data.Data object into positive and negative train/val/test edges.

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

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"). (default: "sum")

segment(src: Tensor, ptr: Tensor, reduce: str = 'sum') → Tensor

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", "mul", "min" or "max"). (default: "sum")

index_sort(inputs: Tensor, max_value: Optional[int] = None) → Tuple[Tensor, Tensor]

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)

degree(index: Tensor, num_nodes: Optional[int] = None, dtype: Optional[dtype] = None) → Tensor

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: Optional[Tensor] = None, ptr: Optional[Tensor] = None, num_nodes: Optional[int] = None, dim: int = 0) → Tensor

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]])

dropout_node(edge_index: Tensor, p: float = 0.5, num_nodes: Optional[int] = None, training: bool = True) → Tuple[Tensor, Tensor, Tensor]

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)

Return type

(LongTensor, BoolTensor, BoolTensor)

Examples

>>> edge_index = torch.tensor([[0, 1, 1, 2, 2, 3],
...                            [1, 0, 2, 1, 3, 2]])
>>> edge_index, edge_mask, node_mask = dropout_node(edge_index)
>>> edge_index
tensor([[0, 1],
        [1, 0]])
>>> edge_mask
tensor([ True,  True, False, False, False, False])
>>> node_mask
tensor([ True,  True, False, False])

dropout_edge(edge_index: Tensor, p: float = 0.5, force_undirected: bool = False, training: bool = True) → Tuple[Tensor, Tensor]

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, edge_mask = dropout_edge(edge_index)
>>> edge_index
tensor([[0, 1, 2, 2],
        [1, 2, 1, 3]])
>>> edge_mask # masks indicating which edges are retained
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: Optional[int] = None, is_sorted: bool = False, training: bool = True) → Tuple[Tensor, Tensor]

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, edge_mask = dropout_path(edge_index)
>>> edge_index
tensor([[1, 2],
        [2, 3]])
>>> edge_mask # masks indicating which edges are retained
tensor([False, False,  True, False,  True, False])

dropout_adj(edge_index: Tensor, edge_attr: Optional[Tensor] = None, p: float = 0.5, force_undirected: bool = False, num_nodes: Optional[int] = None, training: bool = True) → Tuple[Tensor, Optional[Tensor]]

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])
>>> dropout_adj(edge_index, edge_attr)
(tensor([[0, 1, 2, 3],
        [1, 2, 3, 2]]),
tensor([1, 3, 5, 6]))

>>> # The returned graph is kept undirected
>>> dropout_adj(edge_index, edge_attr, force_undirected=True)
(tensor([[0, 1, 2, 1, 2, 3],
        [1, 2, 3, 0, 1, 2]]),
tensor([1, 3, 5, 1, 3, 5]))

shuffle_node(x: Tensor, batch: Optional[Tensor] = None, training: bool = True) → Tuple[Tensor, Tensor]

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) → Tuple[Tensor, Tensor]

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, feat_mask = mask_feature(x)
>>> x
tensor([[1., 0., 3.],
        [4., 0., 6.],
        [7., 0., 9.]]),
>>> feat_mask
tensor([[True, False, True]])

>>> # Masked features are row-wise sampled
>>> x, feat_mask = mask_feature(x, mode='row')
>>> x
tensor([[1., 2., 3.],
        [0., 0., 0.],
        [7., 8., 9.]]),
>>> feat_mask
tensor([[True], [False], [True]])

>>> # Masked features are uniformly sampled
>>> x, feat_mask = mask_feature(x, mode='all')
>>> x
tensor([[0., 0., 0.],
        [4., 0., 6.],
        [0., 0., 9.]])
>>> feat_mask
tensor([[False, False, False],
        [True, False,  True],
        [False, False,  True]])

add_random_edge(edge_index, p: float, force_undirected: bool = False, num_nodes: Optional[Union[int, Tuple[int]]] = None, training: bool = True) → Tuple[Tensor, Tensor]

Randomly adds edges to edge_index.

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.

• 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, added_edges = add_random_edge(edge_index, p=0.5)
>>> edge_index
tensor([[0, 1, 1, 2, 2, 3, 2, 1, 3],
        [1, 0, 2, 1, 3, 2, 0, 2, 1]])
>>> added_edges
tensor([[2, 1, 3],
        [0, 2, 1]])

>>> # The returned graph is kept undirected
>>> edge_index, added_edges = add_random_edge(edge_index, p=0.5,
...                                           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]])
>>> added_edges
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]])
>>> edge_index, added_edges = add_random_edge(edge_index, p=0.5,
...                                           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]])
>>> added_edges
tensor([[3, 4, 1],
        [1, 3, 2]])

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

Row-wise sorts edge_index.

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 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.

Return type

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

Warning

From PyG >= 2.3.0 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: Optional[int] = None, reduce: str = 'add', is_sorted: bool = False, sort_by_row: bool = True) → Union[Tensor, Tuple[Tensor, Optional[Tensor]], Tuple[Tensor, List[Tensor]]]

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 (LongTensor) – The edge indices.

• edge_attr (Tensor or List[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 ("add", "mean", "min", "max", "mul"). (default: "add")

• 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 PyG >= 2.3.0 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: Union[Tensor, None, List[Tensor]] = None, num_nodes: Optional[int] = None) → bool

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_val + 1 of edge_index. (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: Optional[int] = None, reduce: str = 'add') → Union[Tensor, Tuple[Optional[Tensor], Tensor], Tuple[Tensor, List[Tensor]]]

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_val + 1 of edge_index. (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 PyG >= 2.3.0 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

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: Optional[Tensor] = None) → Tuple[Tensor, Optional[Tensor]]

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: Optional[Tensor] = None) → Tuple[Tensor, Optional[Tensor], Tensor, Optional[Tensor]]

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: Optional[Tensor] = None, fill_value: Optional[Union[float, Tensor, str]] = None, num_nodes: Optional[Union[int, Tuple[int, int]]] = None) → Tuple[Tensor, Optional[Tensor]]

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])
>>> add_self_loops(edge_index)
(tensor([[0, 1, 0, 0, 1],
        [1, 0, 0, 0, 1]]),
None)

>>> add_self_loops(edge_index, edge_weight)
(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`
>>> add_self_loops(edge_index, edge_weight,
...                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
>>> add_self_loops(edge_index, edge_weight,
...                fill_value='add')
(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: Optional[Tensor] = None, fill_value: Optional[Union[float, Tensor, str]] = None, num_nodes: Optional[int] = None) → Tuple[Tensor, Optional[Tensor]]

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])
>>> add_remaining_self_loops(edge_index, edge_weight)
(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: Optional[Tensor] = None, num_nodes: Optional[int] = None) → Tensor

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: Optional[int] = None) → bool

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: Optional[Tensor] = None, num_nodes: Optional[int] = None) → Tuple[Tensor, Optional[Tensor], Tensor]

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)
>>> mask # node mask (2 nodes)
tensor([True, True])

>>> edge_index, edge_attr, mask = remove_isolated_nodes(edge_index,
...                                                     num_nodes=3)
>>> mask # node mask (3 nodes)
tensor([True, True, False])

get_num_hops(model: Module) → int

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

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 = torch.F.relu(self.conv1(x, edge_index))
...         x = self.conv2(x, edge_index)
...         return self.lin(x)
>>> get_num_hops(GNN())
2

subgraph(subset: Union[Tensor, List[int]], edge_index: Tensor, edge_attr: Optional[Tensor] = None, relabel_nodes: bool = False, num_nodes: Optional[int] = None, return_edge_mask: bool = False) → Union[Tuple[Tensor, Optional[Tensor]], Tuple[Tensor, Optional[Tensor], Optional[Tensor]]]

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_val + 1 of edge_index. (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.]))

>>> subgraph(subset, edge_index, edge_attr, return_edge_mask=True)
(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: Optional[Tensor] = None, relabel_nodes: bool = False, size: Optional[Tuple[int, int]] = None, return_edge_mask: bool = False) → Union[Tuple[Tensor, Optional[Tensor]], Tuple[Tensor, Optional[Tensor], Optional[Tensor]]]

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,
...                    return_edge_mask=True)
(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: Optional[int] = None, flow: str = 'source_to_target', directed: bool = False) → Tuple[Tensor, Tensor, Tensor, Tensor]

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 False, will include all edges between all sampled nodes. (default: True)

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])
>>> edge_mask
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])
>>> edge_mask
tensor([True, True, True, True])
>>> subset[mapping]
tensor([0, 6])

homophily(edge_index: Union[Tensor, SparseTensor], y: Tensor, batch: Optional[Tensor] = None, method: str = 'edge') → Union[float, Tensor]

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]) → float

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: Optional[Tensor] = None, normalization: Optional[str] = None, dtype: Optional[dtype] = None, num_nodes: Optional[int] = None) → Tuple[Tensor, Optional[Tensor]]

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: Optional[str] = None) → Tuple[Tensor, Tensor]

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 \(\mathbf{L} = \mathbf{M}^{-1} \mathbf{C}\)

mask_select(src: Tensor, dim: int, mask: Tensor) → Tensor

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: Optional[int] = None) → Tensor

Converts indices to a mask representation.

Parameters

• idx (Tensor) – The indices.

• size (int, optional) – minimal sized output mask is returned.

Example

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

>>> index_to_mask(index, size=7)
tensor([False,  True, False,  True, False,  True, False])

mask_to_index(mask: Tensor) → Tensor

Converts a mask to an index representation.

Parameters

mask (Tensor) – The mask.

Example

>>> mask = torch.tensor([False, True, False])
>>> mask_to_index(mask)
tensor([1])

select(src: Union[Tensor, List[Any]], index_or_mask: Tensor, dim: int) → Union[Tensor, List[Any]]

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.

• index_or_mask (torch.Tensor) – The index or mask vector.

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

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

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: Optional[Tensor] = None, fill_value: float = 0.0, max_num_nodes: Optional[int] = None, batch_size: Optional[int] = None) → Tuple[Tensor, Tensor]

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) – 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]])

>>> out, mask = to_dense_batch(x)
>>> mask
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]]])
>>> mask
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]]])

>>> mask
tensor([[ True,  True, False, False],
        [ True, False, False, False],
        [ True,  True,  True, False]])

to_dense_adj(edge_index: Tensor, batch: Optional[Tensor] = None, edge_attr: Optional[Tensor] = None, max_num_nodes: Optional[int] = None, batch_size: Optional[int] = None) → Tensor

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. (default: None)

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

• batch_size (int, optional) – 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])
>>> to_dense_adj(edge_index, batch)
tensor([[[1., 1.],
        [1., 0.]],
        [[0., 1.],
        [1., 0.]]])

>>> to_dense_adj(edge_index, batch, max_num_nodes=4)
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, 2, 3, 4, 5])
>>> to_dense_adj(edge_index, batch, edge_attr)
tensor([[[1., 2.],
        [3., 0.]],
        [[0., 4.],
        [5., 0.]]])

to_nested_tensor(x: Tensor, batch: Optional[Tensor] = None, ptr: Optional[Tensor] = None, batch_size: Optional[int] = None) → 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. 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) – (default: None)

from_nested_tensor(x: Tensor, return_batch: bool = False) → Union[Tensor, Tuple[Tensor, 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. 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)

dense_to_sparse(adj: Tensor) → Tuple[Tensor, Tensor]

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

Parameters

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

Return type

(LongTensor, Tensor)

Examples

>>> # Forr a single adjacency matrix
>>> adj = torch.tensor([[3, 1],
...                     [2, 0]])
>>> dense_to_sparse(adj)
(tensor([[0, 0, 1],
        [0, 1, 0]]),
tensor([3, 1, 2]))

>>> # For two adjacency matrixes
>>> adj = torch.tensor([[[3, 1],
...                      [2, 0]],
...                     [[0, 1],
...                      [0, 2]]])
>>> dense_to_sparse(adj)
(tensor([[0, 0, 1, 2, 3],
        [0, 1, 0, 3, 3]]),
tensor([3, 1, 2, 1, 2]))

is_torch_sparse_tensor(src: Any) → bool

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

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: Optional[Tensor] = None, size: Optional[Union[int, Tuple[int, int]]] = None, is_coalesced: bool = False) → Tensor

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: Optional[Tensor] = None, size: Optional[Union[int, Tuple[int, int]]] = None, is_coalesced: bool = False) → Tensor

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: Optional[Tensor] = None, size: Optional[Union[int, Tuple[int, int]]] = None, is_coalesced: bool = False) → Tensor

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_edge_index(adj: Union[Tensor, SparseTensor]) → Tuple[Tensor, Tensor]

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

Parameters

adj (torch.sparse.Tensor or SparseTensor) – The adjacency matrix.

Return type

(torch.Tensor, torch.Tensor)

Example

>>> edge_index = torch.tensor([[0, 1, 1, 2, 2, 3],
...                            [1, 0, 2, 1, 3, 2]])
>>> adj = to_torch_coo_tensor(edge_index)
>>> to_edge_index(adj)
(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') → Tensor

Matrix product of sparse matrix with dense matrix.

Parameters

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

• other (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) → List[Tensor]

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)

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) → List[Tensor]

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.

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: Optional[int] = None, dtype: Optional[dtype] = None) → Tensor

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: Optional[int] = None) → Tensor

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: Optional[dtype] = None, device: Optional[device] = None) → Tuple[Tensor, Tensor]

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.device, optional) – The desired data type of the returned position tensor.

• dtype – The desired device of the returned tensors.

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: Optional[Tensor] = None, dest: Optional[Tensor] = None, norm: bool = True, max_distance: Optional[float] = None, num_workers: int = 0) → Tensor

Computes (normalized) geodesic distances of a mesh given by pos and face. If src and dest 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 (Tensor) – The node positions.

• face (LongTensor) – The face indices.

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

• dest (LongTensor, 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],
...                     [2, 0, 0],
...                     [0, 2, 0],
...                     [2, 2, 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: Optional[Tensor] = None, num_nodes: Optional[int] = None) → coo_matrix

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) → Tuple[Tensor, Tensor]

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],
... ])
>>> adj = to_scipy_sparse_matrix(edge_index)
>>> # `edge_index` and `edge_weight` are both returned
>>> from_scipy_sparse_matrix(adj)
(tensor([[0, 1, 1, 2, 2, 3],
        [1, 0, 2, 1, 3, 2]]),
tensor([1., 1., 1., 1., 1., 1.]))

to_networkx(data: Data, node_attrs: Optional[Iterable[str]] = None, edge_attrs: Optional[Iterable[str]] = None, graph_attrs: Optional[Iterable[str]] = None, to_undirected: Optional[Union[bool, str]] = False, remove_self_loops: bool = False) → Any

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) – The 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 or “upper”, will return a networkx.Graph instead of a networkx.DiGraph. The undirected graph will correspond to the upper triangle of the corresponding adjacency matrix. Similarly, if set to “lower”, the undirected graph will correspond to the lower triangle of the adjacency matrix. (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], all]] = None, group_edge_attrs: Optional[Union[List[str], all]] = None) → Data

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: Optional[Tensor] = None, num_nodes: Optional[int] = None, directed: bool = True) → Any

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) → Tuple[Tensor, Optional[Tensor]]

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)

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)

Converts a trimesh.Trimesh to a

torch_geometric.data.Data instance.

Args:

mesh (trimesh.Trimesh): A trimesh mesh.

Example

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: Optional[Tensor] = None, relabel_nodes: bool = True, directed: bool = True)

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) → Tuple[Tensor, Optional[Tensor]]

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

Parameters

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

from_smiles(smiles: str, with_hydrogen: bool = False, kekulize: bool = False) → Data

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

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

Parameters

• data (torch_geometric.data.Data) – The molecular graph.

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

erdos_renyi_graph(num_nodes: int, edge_prob: float, directed: bool = False) → Tensor

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) → Tensor

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) → Tensor

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: Optional[int] = None, method: str = 'sparse', force_undirected: bool = False) → Tensor

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: Union[Tensor, Tuple[Tensor, Tensor]], num_neg_samples: Optional[int] = None, method: str = 'sparse', force_undirected: bool = False) → Tensor

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, num_nodes: Optional[int] = None, contains_neg_self_loops: bool = True)

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: Optional[int] = None, contains_neg_self_loops: bool = True) → bool

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

tree_decomposition(mol: Any, return_vocab: bool = False) → Union[Tuple[Tensor, Tensor, int], Tuple[Tensor, Tensor, int, Tensor]]

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, **kwargs) → List[Tensor]

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[Tuple[str, str, str], Tensor]], Union[Tensor, Dict[str, Tensor]], Optional[Union[Tensor, Dict[Tuple[str, str, str], Tensor]]]]

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.

train_test_split_edges(data: Data, val_ratio: float = 0.05, test_ratio: float = 0.1) → Data

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