Optimizing an Organized Modularity Measure for Topographic Graph Clustering: a Deterministic Annealing Approach

TL;DR

This paper introduces a novel organized modularity measure for graph clustering optimized through deterministic annealing, producing topologically ordered clusterings that enhance graph readability and representation.

Contribution

It presents a new organized modularity measure and a deterministic annealing optimization method for topographic graph clustering, improving interpretability over classical approaches.

Findings

Outperforms classical clustering methods in topological ordering

Produces more faithful and readable graph representations

Effective on real-world graphs with up to 1133 vertices

Abstract

This paper proposes an organized generalization of Newman and Girvan's modularity measure for graph clustering. Optimized via a deterministic annealing scheme, this measure produces topologically ordered graph clusterings that lead to faithful and readable graph representations based on clustering induced graphs. Topographic graph clustering provides an alternative to more classical solutions in which a standard graph clustering method is applied to build a simpler graph that is then represented with a graph layout algorithm. A comparative study on four real world graphs ranging from 34 to 1 133 vertices shows the interest of the proposed approach with respect to classical solutions and to self-organizing maps for graphs.