提出新图同质性度量方法，解决不同数据集间比较不准的问题。
Revisiting Graph Homophily Measures
- 设计无偏同质性度量，克服原有方法对类别数量和分布的敏感性
- 理论与实证证明新方法在各类场景下行为稳定可靠
- 指出有向图中理想性质不可共存，揭示度量局限性
同质性是描述图中边连接相似节点倾向的图属性。现有多种同质性度量方法，但均存在缺陷：无法在类别数和类别分布不同的数据集间可靠比较。此前研究提出了理想同质性度量应具备的若干性质，但指出现有方法均不满足全部性质。本文提出一种新度量——无偏同质性（unbiased homophily），该度量满足所有理想性质，可跨不同标签分布的数据集可靠使用。该方法适用于无向（及加权）图。我们通过理论分析和实证例子表明，现有度量存在严重缺陷，而无偏同质性在所考虑场景下表现优异。对于有向图，我们证明某些理想性质相互矛盾，因此不存在同时满足所有性质的度量。
原文摘要 · Abstract (English)
Homophily is a graph property describing the tendency of edges to connect similar nodes. There are several measures used for assessing homophily but all are known to have certain drawbacks: in particular, they cannot be reliably used for comparing datasets with varying numbers of classes and class size balance. To show this, previous works on graph homophily suggested several properties desirable for a good homophily measure, also noting that no existing homophily measure has all these properties. Our paper addresses this issue by introducing a new homophily measure - unbiased homophily - that has all the desirable properties and thus can be reliably used across datasets with different label distributions. The proposed measure is suitable for undirected (and possibly weighted) graphs. We show both theoretically and via empirical examples that the existing homophily measures have serious drawbacks while unbiased homophily has a desirable behavior for the considered scenarios. Finally, when it comes to directed graphs, we prove that some desirable properties contradict each other and thus a measure satisfying all of them cannot exist.
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