Untangling Force-Directed Layouts Using Persistent Homology

TL;DR

This paper introduces a novel approach that applies persistent homology to improve force-directed graph layouts by reducing clutter and enhancing global structure visualization, leading to faster convergence and clearer diagrams.

Contribution

It presents a new method using 0- and 1-dimensional persistent homology to generate initial layouts and interactively highlight structural features, improving layout quality and interpretability.

Findings

Faster convergence of graph layouts.

Enhanced visualization of global structures.

Effective handling of real-world and synthetic graphs.

Abstract

Force-directed layouts belong to a popular class of methods used to position nodes in a node-link diagram. However, they typically lack direct consideration of global structures, which can result in visual clutter and the overlap of unrelated structures. In this paper, we use the principles of persistent homology to untangle force-directed layouts thus mitigating these issues. First, we devise a new method to use 0-dimensional persistent homology to efficiently generate an initial graph layout. The approach results in faster convergence and better quality graph layouts. Second, we provide a new definition and an efficient algorithm for 1-dimensional persistent homology features (i.e., tunnels/cycles) on graphs. We provide users the ability to interact with the 1-dimensional features by highlighting them and adding cycle-emphasizing forces to the layout. Finally, we evaluate our approach with 32 synthetic and real-world graphs by computing various metrics, e.g., co-ranking, edge crossing, etc., to demonstrate the efficacy of our proposed method.