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Metrics for graph comparison: A practitioner’s guide

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  • Peter Wills
  • François G Meyer

Abstract

Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and comparison of structures such as modular communities, rich clubs, hubs, and trees yield insight into the generative mechanisms and functional properties of the graph. Often, two graphs are compared via a pairwise distance measure, with a small distance indicating structural similarity and vice versa. Common choices include spectral distances and distances based on node affinities. However, there has of yet been no comparative study of the efficacy of these distance measures in discerning between common graph topologies at different structural scales. In this work, we compare commonly used graph metrics and distance measures, and demonstrate their ability to discern between common topological features found in both random graph models and real world networks. We put forward a multi-scale picture of graph structure wherein we study the effect of global and local structures on changes in distance measures. We make recommendations on the applicability of different distance measures to the analysis of empirical graph data based on this multi-scale view. Finally, we introduce the Python library NetComp that implements the graph distances used in this work.

Suggested Citation

  • Peter Wills & François G Meyer, 2020. "Metrics for graph comparison: A practitioner’s guide," PLOS ONE, Public Library of Science, vol. 15(2), pages 1-54, February.
  • Handle: RePEc:plo:pone00:0228728
    DOI: 10.1371/journal.pone.0228728
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    References listed on IDEAS

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    1. Javier Rasero & Hannelore Aerts & Marlis Ontivero Ortega & Jesus M Cortes & Sebastiano Stramaglia & Daniele Marinazzo, 2018. "Predicting functional networks from region connectivity profiles in task-based versus resting-state fMRI data," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-18, November.
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    Cited by:

    1. Gabrielle A. Dotson & Can Chen & Stephen Lindsly & Anthony Cicalo & Sam Dilworth & Charles Ryan & Sivakumar Jeyarajan & Walter Meixner & Cooper Stansbury & Joshua Pickard & Nicholas Beckloff & Amit Su, 2022. "Deciphering multi-way interactions in the human genome," Nature Communications, Nature, vol. 13(1), pages 1-15, December.
    2. Nie, Chun-Xiao, 2022. "Generalized correlation dimension and heterogeneity of network spaces," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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