Partitioning Breaks Communities

TL;DR

This paper investigates how graph partitioning algorithms often split cliques across communities, revealing that many networks have overlapping and unpartitionable community structures, challenging traditional community detection assumptions.

Contribution

The study demonstrates that common partitioning methods frequently split cliques and that overlapping community algorithms reveal significant overlaps, highlighting the limitations of partition-based approaches.

Findings

Many cliques are split across communities in empirical networks.

Partitioning algorithms often fail to capture overlapping community structures.

Strong ties and cliques frequently cross community boundaries.

Abstract

Considering a clique as a conservative definition of community structure, we examine how graph partitioning algorithms interact with cliques. Many popular community-finding algorithms partition the entire graph into non-overlapping communities. We show that on a wide range of empirical networks, from different domains, significant numbers of cliques are split across the separate partitions produced by these algorithms. We then examine the largest connected component of the subgraph formed by retaining only edges in cliques, and apply partitioning strategies that explicitly minimise the number of cliques split. We further examine several modern overlapping community finding algorithms, in terms of the interaction between cliques and the communities they find, and in terms of the global overlap of the sets of communities they find. We conclude that, due to the connectedness of many networks, any community finding algorithm that produces partitions must fail to find at least some significant structures. Moreover, contrary to traditional intuition, in some empirical networks, strong ties and cliques frequently do cross community boundaries; much community structure is fundamentally overlapping and unpartitionable in nature.