Modularity clustering is force-directed layout

TL;DR

This paper demonstrates that force-directed layouts and modularity-based clusterings are fundamentally connected through energy models, unifying two common network analysis representations.

Contribution

It shows that energy models of attraction and repulsion encompass modularity, linking layouts and clusterings in network analysis.

Findings

Energy models subsume modularity measure

Optimal energy layouts relate to optimal modularity clusterings

Layouts and clusterings are mutually consistent representations

Abstract

Two natural and widely used representations for the community structure of networks are clusterings, which partition the vertex set into disjoint subsets, and layouts, which assign the vertices to positions in a metric space. This paper unifies prominent characterizations of layout quality and clustering quality, by showing that energy models of pairwise attraction and repulsion subsume Newman and Girvan's modularity measure. Layouts with optimal energy are relaxations of, and are thus consistent with, clusterings with optimal modularity, which is of practical relevance because both representations are complementary and often used together.