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2008

Mixing time of exponential random graphs

Bhamidi, Shankar, Bresler, Guy, Sly, Allan

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Exponential random graphs are used extensively in the sociology literature.

This model seeks to incorporate in random graphs the notion of reciprocity, that is, the larger than expected number of triangles and other small subgraphs.
Sampling from these distributions is crucial for parameter estimation hypothesis testing, and more generally for understanding basic features of the network model itself.
In practice sampling is typically carried out using Markov chain Monte Carlo, in particular either the Glauber dynamics or the Metropolis-Hasting procedure.

Mixing time of exponential random graphs · Around

Built on

Markov graphs
O. Frank and D. Strauss · 1986
Earlier work this paper cites.
Quasi-random graphs
F. R. K. Chung, R. Graham, and R. M. Wilson · 1989
Earlier work this paper cites.
Logit models and logistic regressions for social networks
S. Wasserman and P. Pattison · 1996
Earlier work this paper cites.
Path coupling: A technique for proving rapid mixing in Markov chains
R. Bubley and M. Dyer · 1997
Earlier work this paper cites.
A p* primer: logit models for social networks
C. J. Anderson, S. Wasserman, and B. Crouch · 1999
Earlier work this paper cites.
Statistical mechanics of complex networks
R. Albert and A. L. Barabasi · 2002
Earlier work this paper cites.

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Then

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Mixing time of exponential random graphs
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Closest in time.
Exact large deviations for triangles in a random graph, 2008
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