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Statistical Inference for Complex Networks Workshop, December 3-5, 2008, Santa Fe NM
Edo Airoldi (homepage)
The exchangeable graph model
Collections of pairwise measurements arise in a number of settings in the biological sciences (e.g., www.yeastgenome.org), with collections of scientific publications (e.g., www.jstor.org) and other hyper-linked resources (e.g., www.wikipedia.org), and in social networks (e.g., www.linkedin.com). In this talk we introduce the exchangeable graph model, a simple extension of the random graph model by Erdos & Renyi (1959) and Gilbert (1959). The exchangeable graph model can instantiate realistic connectivity patterns, is amenable to mathematical analysis, and preserves phenomena such as the emergence of a giant component. We demonstrate the utility of the exchangeable graph model in solving two open problems in statistical network analysis: 1. model selection among very different statistical models of pairwise measurements, and 2. assessing the statistical significance associated with the observed overlap of independent cliques in a graph.