Lecture 3: Simulating social networks
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چکیده
(D1+, . . . , DN+) = (d1+, . . . , dN+) def = d+. Let DN,d+ denote the set of all undirected N ×N adjacency matrices with degree counts equal to d+. This note describes an algorithm for sampling uniformly from the set DN,d+ . Sampling uniformly from DN,d+ has a number of uses. First, as we will see later, it facilitates conditional inference on, and conditional estimation of, certain models of network formation. Second, in some settings the researcher may only observe agents’ degree and not their actual links. For example a researcher may know how many friends an individual has, but not who they are. In such cases, properties of the class of networks consistent with the available degree information may be of interest. A concrete example is helpful. Let f (D) be some function of the adjacency matrix, say its transitivity index. Among all undirected networks with degree sequences coinciding with D’s what fraction have a transitivity index less than the one observed in the network in hand? Let ∣∣DN,d+∣∣ denote the size, or cardinality, of DN,d+ . We seek to evaluate
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تاریخ انتشار 2014