2021/05/10 by D. F. Ferguson, Ferguson, Daniel, François G. Meyer +1
Computer Science · Mathematics · #Data Analysis #Data Management and Algorithms #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (stat.ML) #Social and Information Networks (cs.SI) #Statistical Methods and Inference #Statistics and Probability (physics.data-an) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2105.04062
openalex publication_date 2021/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Fréchet 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 Fréchet mean of a set of undirected unweighted graphs with a fixed size.