节点与社区联系的多样性
Versatility of nodal affiliation to communities
摘要：
网络社区结构的图论分析试图识别每个节点所属的社区（或模块）。然而，在大多数情况下，这是一个不适定的问题，因为一个节点到一个社区的从属关系往往是模糊的。以前的解决方案试图识别每个节点所属的所有社区。我们没有采用这种方法，而是引入了多功能性$V$作为节点隶属关系的新指标：$V \sim 0$意味着节点被一致地分配给特定社区; $V \gg 0$意味着它被不一致地分配给不同的社区。多功能性与现有的社区检测算法结合使用，它满足了理想化网络中许多理论上理想的属性，这些理想化网络旨在最大限度地提高模块分解的模糊性。全局平均通用性的局部最小值确定了分层社区检测算法的分辨率参数，该算法最不含糊地分解了社交（空手道俱乐部）网络和小鼠大脑连接体的社区结构。我们的研究结果表明，节点的多功能性是有用的量化模块化分解的固有的模糊性。
英文摘要：
Graph theoretical analysis of the community structure of networks attempts to identify the communities (or modules) to which each node affiliates. However, this is in most cases an ill-posed problem, as the affiliation of a node to a single community is often ambiguous. Previous solutions have attempted to identify all of the communities to which each node affiliates. Instead of taking this approach, we introduce versatility, $V$, as a novel metric of nodal affiliation: $V \sim 0$ means that a node is consistently assigned to a specific community; $V \gg 0$ means it is inconsistently assigned to different communities. Versatility works in conjunction with existing community detection algorithms, and it satisfies many theoretically desirable properties in idealised networks designed to maximise ambiguity of modular decomposition. The local minima of global mean versatility identified the resolution parameters of a hierarchical community detection algorithm that least ambiguously decomposed the community structure of a social (karate club) network and the mouse brain connectome. Our results suggest that nodal versatility is useful in quantifying the inherent ambiguity of modular decomposition.
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