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"""Utils for tacking graph homophily and heterophily""" | ||
from . import backend as F | ||
from . import function as fn | ||
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__all__ = ['node_homophily'] | ||
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def node_homophily(graph, y): | ||
"""Homophily measure from `Geom-GCN: Geometric Graph Convolutional Networks | ||
<https://arxiv.org/abs/2002.05287>`__ | ||
We follow the practice of a later paper `Large Scale Learning on | ||
Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods | ||
<https://arxiv.org/abs/2110.14446>`__ to call it node homophily. | ||
Mathematically it is defined as follows: | ||
.. math:: | ||
\frac{1}{|\mathcal{V}|} \sum_{v \in \mathcal{V}} \frac{ | \{ (u,v) : u | ||
\in \mathcal{N}(v) \wedge y_v = y_u \} | } { |\mathcal{N}(v)| } | ||
where :math:`\mathcal{V}` is the set of nodes, :math:`\mathcal{N}(v)` is | ||
the predecessors of node :math:`v`, and :math:`y_v` is the class of node | ||
:math:`v`. | ||
Parameters | ||
---------- | ||
graph : DGLGraph | ||
The graph | ||
y : Tensor | ||
The node labels, which is a tensor of shape (|V|) | ||
Returns | ||
------- | ||
float | ||
The node homophily value | ||
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 | ||
""" | ||
with graph.local_scope(): | ||
src, dst = graph.edges() | ||
# Handle the case where graph is of dtype int32. | ||
src = F.astype(src, F.int64) | ||
dst = F.astype(dst, F.int64) | ||
# Compute y_v = y_u for all edges. | ||
graph.edata['same_class'] = F.astype(y[src] == y[dst], F.float32) | ||
graph.update_all(fn.copy_e('same_class', 'm'), | ||
fn.mean('m', 'node_value')) | ||
return graph.ndata['node_value'].mean().item() |
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import backend as F | ||
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import dgl | ||
from test_utils import parametrize_idtype | ||
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@parametrize_idtype | ||
def test_node_homophily(idtype): | ||
# NOTE: If you want to update this test case, remember to update the | ||
# docstring example too. | ||
device = F.ctx() | ||
g = dgl.graph(([1, 2, 0, 4], [0, 1, 2, 3]), idtype=idtype, device=device) | ||
y = F.tensor([0, 0, 0, 0, 1]) | ||
assert dgl.node_homophily(graph, y) == 0.6000000238418579 |