Metrics for Graph Comparison: A Practitioner’s Guide Peter Wills1 , Fran¸cois G. Meyer1* , 1 Applied Mathematics, University of Colorado at Boulder, Boulder CO 80305 * fmeyer@colorado.edu arXiv:1904.07414v1 [stat.AP] 16 Apr 2019 Abstract Comparison of graph...
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Metrics for Graph Comparison: A Practitioner’s Guide Peter Wills1 , Fran¸cois G. Meyer1* , 1 Applied Mathematics, University of Colorado at Boulder, Boulder CO 80305 * fmeyer@colorado.edu arXiv:1904.07414v1 [stat.AP] 16 Apr 2019 Abstract Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience [1], cyber security [2], social network analysis [3], and bioinformatics [4], among others. Discovery and comparison of structures such as modular communities, rich clubs, hubs, and trees in data in these fields yields 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 (also known as λ distances) and distances based on node affinities (such as DeltaCon [5]). However, there has of yet been no comparative stu
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