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Network Models in Probability and Statistics

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International Encyclopedia of Statistical Science

A network is a representation for a collection of individuals or other unitsconnected in a pairwise fashion by relationships, such as friendship. Networks aretypically displayed visually as “graphs,” so that individuals correspond to the“nodes” of a graph, with the existence of a relationship indicated by an edgebetween pairs of nodes. Relationships can be univariate or multivariate,and the connections between individuals can be either directed (fromone to the other) or undirected. In terms of statistical science, a networkmodel is one that accounts for the structure of the network ties in terms ofthe probability that each network tie exists, whether conditional on allother ties, or as considered part of the distribution of the ensemble of ties.

A network with N nodes has \((_2^N )\) unordered pairs of nodes, and hence \(2(_2^N )\) possible directed edges. If the labels on edges reflect the nodes they link, as(i,j), Y ij represents the existence of an edge from individual i to j, and \(...

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Fienberg, S.E., Thomas, A.C. (2011). Network Models in Probability and Statistics. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_403

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