“An Introduction to Exponential Random Graph Models for Social Networks,” G. Robins et al (2007)

From a special issue on model building in the journal Social Networks, this paper by Robins et al discusses statistical modeling of networks as a tool both to identify whether structures in network data are due to chance or not, and as a way to model hypotheses about the global effects of local network structures. There is a good background on the ERG, or p* model, which allows a very flexible modeling of dependence relations among edges in the graph (for instance, balance theory). The essential result of ERG is the Hammersley-Clifford Theorem, which states that IFF a graph is Markovian, in that the probability of a tie between two nodes is dependent only on a local subset of the full graph, then the probability of the tie can be expressed as an exponential function of the hypothesized local dependencies.

http://www.sna.unimelb.edu.au/publications/ERGM11.1.pdf

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