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The method of moments and degree distributions for network models. (English) Zbl 1232.91577
Summary: Probability models on graphs are becoming increasingly important in many applications, but statistical tools for fitting such models are not yet well developed. Here we propose a general method of moments approach that can be used to fit a large class of probability models through empirical counts of certain patterns in a graph. We establish some general asymptotic properties of empirical graph moments and prove consistency of the estimates as the graph size grows for all ranges of the average degree including $$\Omega (1)$$. Additional results are obtained for the important special case of degree distributions.

##### MSC:
 91D30 Social networks; opinion dynamics 62E10 Characterization and structure theory of statistical distributions 62G05 Nonparametric estimation
##### Keywords:
social networks; block model; community detection
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##### References:
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