# torch_geometric.utils¶

degree(index, 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. Tensor
softmax(src, index, num_nodes=None)[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) – The indices of elements for applying the softmax. num_nodes (int, optional) – The number of nodes, i.e. max_val + 1 of index. (default: None) Tensor
dropout_adj(edge_index, edge_attr=None, p=0.5, force_undirected=False, num_nodes=None, training=True)[source]

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

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)
sort_edge_index(edge_index, edge_attr=None, num_nodes=None)[source]

Row-wise sorts edge indices edge_index.

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) (LongTensor, Tensor)
is_undirected(edge_index, edge_attr=None, num_nodes=None)[source]

Returns True if the graph given by edge_index is undirected.

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) bool
to_undirected(edge_index, num_nodes=None)[source]

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

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) LongTensor
contains_self_loops(edge_index)[source]

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

Parameters: edge_index (LongTensor) – The edge indices. bool
remove_self_loops(edge_index, 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) (LongTensor, Tensor)
segregate_self_loops(edge_index, 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) (LongTensor, Tensor, LongTensor, Tensor)
add_self_loops(edge_index, edge_weight=None, fill_value=1, num_nodes=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, self-loops will be added with edge weights denoted by fill_value.

Parameters: edge_index (LongTensor) – The edge indices. edge_weight (Tensor, optional) – One-dimensional edge weights. (default: None) fill_value (int, optional) – If edge_weight is not None, will add self-loops with edge weights of fill_value to the graph. (default: 1) num_nodes (int, optional) – The number of nodes, i.e. max_val + 1 of edge_index. (default: None) (LongTensor, Tensor)
add_remaining_self_loops(edge_index, edge_weight=None, fill_value=1, 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 and already contains a few self-loops, only non-existent self-loops will be added with edge weights denoted by fill_value.

Parameters: edge_index (LongTensor) – The edge indices. edge_weight (Tensor, optional) – One-dimensional edge weights. (default: None) fill_value (int, optional) – If edge_weight is not None, will add self-loops with edge weights of fill_value to the graph. (default: 1) num_nodes (int, optional) – The number of nodes, i.e. max_val + 1 of edge_index. (default: None) (LongTensor, Tensor)
contains_isolated_nodes(edge_index, num_nodes=None)[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) bool
remove_isolated_nodes(edge_index, 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) (LongTensor, Tensor, BoolTensor)
subgraph(subset, edge_index, edge_attr=None, relabel_nodes=False, num_nodes=None)[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_val + 1 of edge_index. (default: None) (LongTensor, Tensor)
k_hop_subgraph(node_idx, num_hops, edge_index, relabel_nodes=False, num_nodes=None, flow='source_to_target')[source]

Computes the $$k$$-hop subgraph of edge_index around node node_idx. It 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 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 (string, optional) – The flow direction of $$k$$-hop aggregation ("source_to_target" or "target_to_source"). (default: "source_to_target") (LongTensor, LongTensor, LongTensor, BoolTensor)
get_laplacian(edge_index, 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)
to_dense_batch(x, batch=None, fill_value=0, max_num_nodes=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 second tensor holding $$[N_1, \ldots, N_B] \in \mathbb{N}^B$$ is returned.

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. (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) (Tensor, BoolTensor)
to_dense_adj(edge_index, batch=None, edge_attr=None, max_num_nodes=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. (default: None) max_num_nodes (int, optional) – The size of the output node dimension. (default: None) Tensor
dense_to_sparse(tensor)[source]

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

Parameters: tensor – The dense adjacency matrix.
normalized_cut(edge_index, edge_attr, 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) Tensor
grid(height, width, 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.device, optional) – The desired data type of the returned position tensor. dtype – The desired device of the returned tensors. (LongTensor, Tensor)
geodesic_distance(pos, face, src=None, dest=None, norm=True, max_distance=None, num_workers=0)[source]

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) Tensor
tree_decomposition(mol, return_vocab=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) – A rdkit molecule. return_vocab (bool, optional) – If set to True, will return an identifier for each clique (ring, bond, bridged compounds, single). (default: False) (LongTensor, LongTensor, int)
to_scipy_sparse_matrix(edge_index, edge_attr=None, num_nodes=None)[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)
from_scipy_sparse_matrix(A)[source]

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

Parameters: A (scipy.sparse) – A sparse matrix.
to_networkx(data, node_attrs=None, edge_attrs=None, to_undirected=False, remove_self_loops=False)[source]

Converts a torch_geometric.data.Data instance to a networkx.DiGraph if to_undirected is set to True, or an undirected networkx.Graph 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) to_undirected (bool, optional) – If set to True, will return a a networkx.Graph instead of a networkx.DiGraph. The undirected graph will correspond to the upper triangle of the corresponding adjacency matrix. (default: False) remove_self_loops (bool, optional) – If set to True, will not include self loops in the resulting graph. (default: False)
from_networkx(G)[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.
to_trimesh(data)[source]

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

Parameters: data (torch_geometric.data.Data) – The data object.
from_trimesh(mesh)[source]

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

Parameters: mesh (trimesh.Trimesh) – A trimesh mesh.
erdos_renyi_graph(num_nodes, edge_prob, directed=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)
stochastic_blockmodel_graph(block_sizes, edge_probs, directed=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 each block to each other block. Must be symmetric if the graph is (from) – undirected. directed (bool, optional) – If set to True, will return a directed graph. (default: False)
barabasi_albert_graph(num_nodes, num_edges)[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.
negative_sampling(edge_index, num_nodes=None, num_neg_samples=None, method='sparse', force_undirected=False)[source]

Samples random negative edges of a graph given by edge_index.

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) 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 (string, 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) LongTensor
structured_negative_sampling(edge_index, num_nodes=None)[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) (LongTensor, LongTensor, LongTensor)
batched_negative_sampling(edge_index, batch, num_neg_samples=None, method='sparse', force_undirected=False)[source]

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

Parameters: edge_index (LongTensor) – The edge indices. batch (LongTensor) – Batch vector $$\mathbf{b} \in {\{ 0, \ldots, B-1\}}^N$$, which assigns each node to a specific example. 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 (string, 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) LongTensor
train_test_split_edges(data, val_ratio=0.05, test_ratio=0.1)[source]

Splits the edges of a torch_geometric.data.Data object into positive and negative train/val/test edges, and adds attributes of train_pos_edge_index, train_neg_adj_mask, val_pos_edge_index, val_neg_edge_index, test_pos_edge_index, and test_neg_edge_index to data.

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) torch_geometric.data.Data
accuracy(pred, target)[source]

Computes the accuracy of predictions.

Parameters: pred (Tensor) – The predictions. target (Tensor) – The targets. int
true_positive(pred, target, num_classes)[source]

Computes the number of true positive predictions.

Parameters: pred (Tensor) – The predictions. target (Tensor) – The targets. num_classes (int) – The number of classes. LongTensor
true_negative(pred, target, num_classes)[source]

Computes the number of true negative predictions.

Parameters: pred (Tensor) – The predictions. target (Tensor) – The targets. num_classes (int) – The number of classes. LongTensor
false_positive(pred, target, num_classes)[source]

Computes the number of false positive predictions.

Parameters: pred (Tensor) – The predictions. target (Tensor) – The targets. num_classes (int) – The number of classes. LongTensor
false_negative(pred, target, num_classes)[source]

Computes the number of false negative predictions.

Parameters: pred (Tensor) – The predictions. target (Tensor) – The targets. num_classes (int) – The number of classes. LongTensor
precision(pred, target, num_classes)[source]

Computes the precision $$\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FP}}$$ of predictions.

Parameters: pred (Tensor) – The predictions. target (Tensor) – The targets. num_classes (int) – The number of classes. Tensor
recall(pred, target, num_classes)[source]

Computes the recall $$\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FN}}$$ of predictions.

Parameters: pred (Tensor) – The predictions. target (Tensor) – The targets. num_classes (int) – The number of classes. Tensor
f1_score(pred, target, num_classes)[source]

Computes the $$F_1$$ score $$2 \cdot \frac{\mathrm{precision} \cdot \mathrm{recall}} {\mathrm{precision}+\mathrm{recall}}$$ of predictions.

Parameters: pred (Tensor) – The predictions. target (Tensor) – The targets. num_classes (int) – The number of classes. Tensor
intersection_and_union(pred, target, num_classes, batch=None)[source]

Computes intersection and union of predictions.

Parameters: pred (LongTensor) – The predictions. target (LongTensor) – The targets. num_classes (int) – The number of classes. batch (LongTensor) – The assignment vector which maps each pred-target pair to an example. (LongTensor, LongTensor)
mean_iou(pred, target, num_classes, batch=None)[source]

Computes the mean intersection over union score of predictions.

Parameters: pred (LongTensor) – The predictions. target (LongTensor) – The targets. num_classes (int) – The number of classes. batch (LongTensor) – The assignment vector which maps each pred-target pair to an example. Tensor