Degeneracy in sparse ERGMs with functions of degrees as sufficient statistics

30 May 2019  ·  Mukherjee Sumit ·

A sufficient criterion for "non-degeneracy" is given for Exponential Random Graph Models on sparse graphs with sufficient statistics which are functions of the degree sequence. This criterion explains why statistics such as alternating $k$-star are non-degenerate, whereas subgraph counts are degenerate... It is further shown that this criterion is "almost" tight. Existence of consistent estimates is then proved for non-degenerate Exponential Random Graph Models. read more

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Probability