Approximate Fr'echet Mean for Data Sets of Sparse Graphs
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Abstract (arXiv)
To characterize the location (mean, median) of a set of graphs, one needs a notion of centrality that is adapted to metric spaces, since graph sets are not Euclidean spaces. A standard approach is to consider the Fr'echet mean. In this work, we equip a set of graph with the pseudometric defined by the ℓ2 norm between the eigenvalues of their respective adjacency matrix . Unlike the edit distance, this pseudometric reveals structural changes at multiple scales, and is well adapted to studying various statistical problems on sets of graphs. We describe an algorithm to compute an approximation to the Fr'echet mean of a set of undirected unweighted graphs with a fixed size.
Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 9 of its 35 references that are in the map. First posted on arXiv 10 May 2021.
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References · 9
- 2017Community Detection and Stochastic Block Modelscited by 317
- 2016Fr'echet Regression for Random Objects with Euclidean Predictorscited by 57
- 2019Metrics for Graph Comparison: A Practitioner's Guidecited by 37
- 2013Network histograms and universality of blockmodel approximationcited by 20
- 2014Hypothesis Testing For Network Data in Functional Neuroimagingcited by 20
- 2019Modeling Network Populations via Graph Distancescited by 13
- 2018The eigenvalues of stochastic blockmodel graphscited by 7
- 2018Spectral Graph Forge: Graph Generation Targeting Modularitycited by 5
- 2019Spectral Representations of Graphons in Very Large Network Systems Controlcited by 3
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