Persistent Homology Guided Force-Directed Graph Layouts

Ashley Suh, Mustafa Hajij, Bei Wang, Carlos Scheidegger, Paul Rosen

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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.

Original languageEnglish (US)
Article number8807379
Pages (from-to)697-707
Number of pages11
JournalIEEE Transactions on Visualization and Computer Graphics
Issue number1
StatePublished - Jan 2020
Externally publishedYes


  • Graph drawing
  • Topological Data Analysis
  • force-directed layout
  • persistent homology

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Computer Graphics and Computer-Aided Design


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