Versatility of nodal affiliation to communities

TL;DR

This paper introduces versatility, a new metric for assessing how consistently nodes affiliate with communities in networks, helping to quantify ambiguity in community detection.

Contribution

It proposes versatility as a novel metric that complements existing algorithms to measure nodal affiliation ambiguity in network community structures.

Findings

Versatility effectively quantifies node affiliation ambiguity.

It helps identify optimal resolution parameters in hierarchical community detection.

Versatility is applicable to social and brain connectome networks.

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: $V \sim 0$ 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.