Degeneracy in sparse ERGMs with functions of degrees as sufficient statistics

Sumit Mukherjee

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arXiv · 1310.4160

Degeneracy in sparse ERGMs with functions of degrees as sufficient statistics

Sumit Mukherjee

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Abstract

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.

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Sumit Mukherjee. 2013-10-15. Degeneracy in sparse ERGMs with functions of degrees as sufficient statistics. https://arxiv.org/abs/1310.4160

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