Abstract
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.
Highlights
The community structure of a network divides the network into groups, or communities, which share topological similarity
Our approach to the issue of community ambiguity is predicated on the observation that, the community structure of a network may not be certainly known, there will generally be variability between nodes in terms of the certainty with which they can be individually affiliated with a specific community
We first define an estimator of nodal versatility of community affiliation and demonstrate its desirable properties by analysis of idealised networks designed for maximal community ambiguity
Summary
The community structure of a network divides the network into groups, or communities, which share topological similarity. Various forms of consensus clustering[3, 4] have been developed to optimise non-overlapping modular decomposition “on average” over an ensemble of datasets or runs of a non-deterministic community detection algorithm It remains debatable whether these communities represent the “true” communities of the network, or just the best possible consensus solution given the algorithm and the available data. To build intuitive understanding of what versatility is measuring, we explored its performance in two real-life networks: the karate club graph, a social network; and the mouse brain connectome, a brain network derived from anatomical tract-tracing experiments In both of these cases, we show how versatility can be used to identify the resolution parameters of the Louvain hierarchical community detection algorithm[5] that provide the least ambiguous modular decomposition of the network as a whole. We use versatility to characterise the topological roles of each individual node
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