Metrics for graph comparison: A practitioner's guide

• Published in: PloS one 2020-02, Vol.15 (2), p.e0228728-e0228728
• Main Authors: Wills, Peter, Meyer, François G
• Format: Article
• Language: English
• Subjects: Applied mathematics; Big Data; Bioinformatics; Biology and Life Sciences; Comparative analysis; Comparative literature; Comparative studies; Computational biology; Computer and Information Sciences; Computer Graphics; Computer programs; Computer security; Cybersecurity; Cyberterrorism; Data analysis; Datasets; Distance measurement; Ecology and Environmental Sciences; Empirical analysis; Engineering and Technology; Graph comparison; Graphs; Information management; Internet security; Learning algorithms; Machine learning; Medicine and Health Sciences; Models, Theoretical; Modular structures; Multiscale analysis; Nervous system; Network analysis; Neurosciences; Physical Sciences; Research and Analysis Methods; Security; Social networks; Social organization; Social Sciences; Topology
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0228728

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.