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To characterize the location (mean, median) of a set of graphs, one needs anotion of centrality that is adapted to metric spaces, since graph sets are notEuclidean spaces. A standard approach is to consider the Frechet mean. In thiswork, we equip a set of graphs with the pseudometric defined by the normbetween the eigenvalues of their respective adjacency matrix. Unlike the editdistance, this pseudometric reveals structural changes at multiple scales, andis well adapted to studying various statistical problems for graph-valued data.We describe an algorithm to compute an approximation to the sample Frechet meanof a set of undirected unweighted graphs with a fixed size using thispseudometric.

Theoretical analysis and computation of the sample Frechet mean for sets of large graphs based on spectral information