dgl.node_homophily

dgl.node_homophily(graph, y)

Homophily measure from Geom-GCN: Geometric Graph Convolutional Networks

We follow the practice of a later paper Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods to call it node homophily.

Mathematically it is defined as follows:

$$\frac{1}{|\mathcal{V}|}\sum _{v\in \mathcal{V}}\frac{|\{u\in \mathcal{N}(v):y_v=y_u\}|}{|\mathcal{N}(v)|},$$

where $\mathcal{V}$ is the set of nodes, $\mathcal{N}(v)$ is the predecessors of node $v$, and $y_v$ is the class of node $v$.

Parameters:

• graph (DGLGraph) – The graph.

• y (torch.Tensor) – The node labels, which is a tensor of shape (|V|).

Returns:

The node homophily value.

Return type:

float

Examples

>>> import dgl
>>> import torch

>>> graph = dgl.graph(([1, 2, 0, 4], [0, 1, 2, 3]))
>>> y = torch.tensor([0, 0, 0, 0, 1])
>>> dgl.node_homophily(graph, y)
0.6000000238418579