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Definition

Formal Definition of Graph Generation Evaluation

Given a set of graph statistics S=(s1,s2,,sn)S = (s_1, s_2, \dots, s_n) (which can include degree statistics, clustering coefficients, or motif/graphlet counts), compute each statistic sis_i for both the generated graphs and a test graph. Next, compute the distance between the statistics' distributions on the test graph and generated graph using a distributional measure, such as the total variation distance: d(s_{i,G_{test}}, s_{i,G_{gen}}) = sup_{x in mathbb{R}} |s_{i,G_{test}}(x) - s_{i,G_{gen}}(x)|. Finally, compute the average pairwise distributional distance between a set of generated graphs and graphs in a test set for each statistic siSs_i \in S.

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Updated 2026-06-15

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Data Science