Goodness of fit tests for random multigraph models

Goodness of fit tests for two probabilistic multigraph models are presented. The first model is random stub matching given fixed degrees (RSM) so that edge assignments to vertex pair sites dependent, and the second independent (IEA) according a common probability distribution. Tests performed using goodness measures between multiplicity sequence an observed multigraph, expected one simple or composite hypothesis. Test statistics Pearson type likelihood ratio used, values statistic under different derived. performances based on simulations indicate even small number edges, null distributions both well approximated by their asymptotic χ2-distribution. non-null test can be proposed adjusted χ2-distributions used power approximations. influence RSM substantial edges implies shift towards smaller compared what holds true IEA. Two applications social networks included illustrate how guide in analysis structure.