边缘加权容忍社区检测分辨率极限
Tolerating the Community Detection Resolution Limit with Edge Weighting
摘要：
像万维网这样的巨型网络中的顶点社区很可能比网络本身小得多。然而，Mrsanato和Barthélemy已经证明，用于社区检测的模块化最大化算法可能无法解决具有少于$\sqrt{L/2}$边的社区，其中$L$是整个网络中的边的数量。这种分辨率限制导致模块度最大化算法在许多真实网络上的准确性非常差。Rumanato和Barthélemy的论证也可以扩展到带权边的网络，我们推导出这个推论。我们的结论是，加权模块化算法可能无法解决社区小于$\sqrt{W ε/2}$总边的重量，其中$W$是在网络中的总边的重量和$ε$是一个社区间边的最大重量。如果$ε$很小，那么可以解决小社区。给定一个加权或未加权的网络，我们描述了如何获得新的边权重，以实现低$ε$，我们修改了"CNM"社区检测算法，以最大限度地提高加权模块化，并表明，由此产生的算法有很大的提高准确性。在一个新兴的社区标准基准的实验中，我们发现我们简单的CNM变体与最准确的社区检测方法相比具有竞争力。
英文摘要：
Communities of vertices within a giant network such as the World-Wide Web are likely to be vastly smaller than the network itself. However, Fortunato and Barthélemy have proved that modularity maximization algorithms for community detection may fail to resolve communities with fewer than $\sqrt{L/2}$ edges, where $L$ is the number of edges in the entire network. This resolution limit leads modularity maximization algorithms to have notoriously poor accuracy on many real networks. Fortunato and Barthélemy's argument can be extended to networks with weighted edges as well, and we derive this corollary argument. We conclude that weighted modularity algorithms may fail to resolve communities with fewer than $\sqrt{W ε/2}$ total edge weight, where $W$ is the total edge weight in the network and $ε$ is the maximum weight of an inter-community edge. If $ε$ is small, then small communities can be resolved. Given a weighted or unweighted network, we describe how to derive new edge weights in order to achieve a low $ε$, we modify the ``CNM'' community detection algorithm to maximize weighted modularity, and show that the resulting algorithm has greatly improved accuracy. In experiments with an emerging community standard benchmark, we find that our simple CNM variant is competitive with the most accurate community detection methods yet proposed.
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