Department of Psychiatry, Behavioural and Clinical Neuroscience Institute, University of Cambridge, Cambridge, CB2 0SZ, United Kingdom.
Developmental Neurogenomics Unit, National Institute of Mental Health, Bethesda, MD, 20892, USA.
Sci Rep. 2017 Jun 27;7(1):4273. doi: 10.1038/s41598-017-03394-5.
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 ≈ 0 means that a node is consistently assigned to a specific community; V >> 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.
网络的社区结构的图论分析试图确定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，因为节点属于单个社区的归属通常是模糊的。以前的解决方案试图确定每个节点所属的所有社区。我们引入多功能性 V 作为节点归属的新指标，而不是采用这种方法：V≈0 表示节点始终被分配到特定的社区；V>>0 表示节点被不一致地分配到不同的社区。多功能性与现有的社区检测算法相结合，并在旨在最大化模块化分解歧义的理想网络中满足许多理论上理想的属性。全局平均多功能性的局部最小值确定了层次社区检测算法的分辨率参数，该算法最清晰地分解了社交（空手道俱乐部）网络和老鼠大脑连接组的社区结构。我们的结果表明，节点多功能性可用于量化模块化分解的固有歧义。
