torch_geometric.utils

degree(index, num_nodes=None, dtype=None)

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

scatter_(name, src, index, dim=0, dim_size=None)

Aggregates all values from the src tensor at the indices specified in the index tensor along the first dimension. If multiple indices reference the same location, their contributions are aggregated according to name (either "add", "mean" or "max").

Parameters

• name (string) – The aggregation to use ("add", "mean", "min", "max").

• src (Tensor) – The source tensor.

• index (LongTensor) – The indices of elements to scatter.

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

• dim_size (int, optional) – Automatically create output tensor with size dim_size in the first dimension. If set to None, a minimal sized output tensor is returned. (default: None)

Return type

Tensor

softmax(src, index, num_nodes=None)

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)

Return type

Tensor

dropout_adj(edge_index, edge_attr=None, p=0.5, force_undirected=False, num_nodes=None, training=True)

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)

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)

Return type

(LongTensor, Tensor)

is_undirected(edge_index, edge_attr=None, num_nodes=None)

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)

Return type

bool

to_undirected(edge_index, num_nodes=None)

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)

Return type

LongTensor

contains_self_loops(edge_index)

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

Parameters

edge_index (LongTensor) – The edge indices.

Return type

bool

remove_self_loops(edge_index, edge_attr=None)

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)

segregate_self_loops(edge_index, edge_attr=None)

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)

add_self_loops(edge_index, edge_weight=None, fill_value=1, num_nodes=None)

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)

Return type

(LongTensor, Tensor)

add_remaining_self_loops(edge_index, edge_weight=None, fill_value=1, num_nodes=None)

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)

Return type

(LongTensor, Tensor)

contains_isolated_nodes(edge_index, num_nodes=None)

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

remove_isolated_nodes(edge_index, edge_attr=None, num_nodes=None)

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)

subgraph(subset, edge_index, edge_attr=None, relabel_nodes=False, num_nodes=None)

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 type

(LongTensor, Tensor)

get_laplacian(edge_index, edge_weight=None, normalization=None, dtype=None, num_nodes=None)

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)

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)

Return type

(Tensor, BoolTensor)

to_dense_adj(edge_index, batch=None, edge_attr=None)

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)

Return type

Tensor

dense_to_sparse(tensor)

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)

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

grid(height, width, dtype=None, device=None)

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)

geodesic_distance(pos, face, src=None, dest=None, norm=True, max_distance=None)

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)

Return type

Tensor

to_scipy_sparse_matrix(edge_index, edge_attr=None, num_nodes=None)

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)

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)

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)

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)

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

Parameters

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

from_trimesh(mesh)

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)

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)

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)

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, force_undirected=False)

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 number of negative samples to return. If set to None, will try to return a negative edge for every positive edge. (default: None)

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

Return type

LongTensor

structured_negative_sampling(edge_index, num_nodes=None)

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)

Return type

(LongTensor, LongTensor, LongTensor)

batched_negative_sampling(edge_index, batch, num_neg_samples=None, force_undirected=False)

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)

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

Return type

LongTensor

train_test_split_edges(data, val_ratio=0.05, test_ratio=0.1)

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)

Return type

torch_geometric.data.Data

accuracy(pred, target)

Computes the accuracy of predictions.

Parameters

• pred (Tensor) – The predictions.

• target (Tensor) – The targets.

Return type

int

true_positive(pred, target, num_classes)

Computes the number of true positive predictions.

Parameters

• pred (Tensor) – The predictions.

• target (Tensor) – The targets.

• num_classes (int) – The number of classes.

Return type

LongTensor

true_negative(pred, target, num_classes)

Computes the number of true negative predictions.

Parameters

• pred (Tensor) – The predictions.

• target (Tensor) – The targets.

• num_classes (int) – The number of classes.

Return type

LongTensor

false_positive(pred, target, num_classes)

Computes the number of false positive predictions.

Parameters

• pred (Tensor) – The predictions.

• target (Tensor) – The targets.

• num_classes (int) – The number of classes.

Return type

LongTensor

false_negative(pred, target, num_classes)

Computes the number of false negative predictions.

Parameters

• pred (Tensor) – The predictions.

• target (Tensor) – The targets.

• num_classes (int) – The number of classes.

Return type

LongTensor

precision(pred, target, num_classes)

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.

Return type

Tensor

recall(pred, target, num_classes)

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.

Return type

Tensor

f1_score(pred, target, num_classes)

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.

Return type

Tensor

intersection_and_union(pred, target, num_classes, batch=None)

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.

Return type

(LongTensor, LongTensor)

mean_iou(pred, target, num_classes, batch=None)

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.

Return type

Tensor