Reproducing the first and second moments of empirical degree distributions
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摘要
This work proposes a minimal, non-linear exponential random graph model (fit2SM) that can reproduce both the first and second moments of empirical degree distributions within a canonical framework [page::0]. By replacing linear two-star constraints with fitness-induced components, the model avoids the degeneracy of the mean-field two-star approach and successfully matches the sample variance of degree distributions [page::3][page::4]. Empirical validation on the eMID interbank network across daily to yearly aggregations shows that fit2SM outperforms the traditional UBCM and the density-corrected gravity model (dcGM) in reproducing variance, degree sequence, and spectral properties, particularly in sparser configurations [page::2][page::5][page::17]. Moreover, when treated as a generative model, fit2SM supports robust early-warning signal analyses, aligning well with ground-truth indicators even when the true topology is not available [page::8].
