Persistent Homology Guided Force-Directed Graph Layouts

TL;DR

This paper introduces a method that uses persistent homology features to guide force-directed graph layouts, improving visualization clarity by reducing clutter and overlap.

Contribution

It presents an efficient way to extract persistent homology features and an interactive system to manipulate graph layouts based on these features.

Findings

Enhanced graph visualization clarity

Effective reduction of clutter and overlaps

Applicability to synthetic and real datasets

Abstract

Graphs are commonly used to encode relationships among entities, yet their abstractness makes them difficult to analyze. Node-link diagrams are popular for drawing graphs, and force-directed layouts provide a flexible method for node arrangements that use local relationships in an attempt to reveal the global shape of the graph. However, clutter and overlap of unrelated structures can lead to confusing graph visualizations. This paper leverages the persistent homology features of an undirected graph as derived information for interactive manipulation of force-directed layouts. We first discuss how to efficiently extract 0-dimensional persistent homology features from both weighted and unweighted undirected graphs. We then introduce the interactive persistence barcode used to manipulate the force-directed graph layout. In particular, the user adds and removes contracting and repulsing forces generated by the persistent homology features, eventually selecting the set of persistent homology features that most improve the layout. Finally, we demonstrate the utility of our approach across a variety of synthetic and real datasets.