منابع مشابه
Polytopes from Subgraph Statistics
We study polytopes that are convex hulls of vectors of subgraph densities. Many graph theoretical questions can be expressed in terms of these polytopes, and statisticians use them to understand exponential random graph models. Relations among their Ehrhart polynomials are described, their duals are applied to certify that polynomials are nonnegative, and we find some of their faces. For the ge...
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Let H be a fixed graph and G a subcritical graph class. In this paper we show that the number of occurrences of H (as a subgraph) in a uniformly at random graph of size n in G follows a normal limiting distribution with linear expectation and variance. The main ingredient in our proof is the analytic framework developed by Drmota, Gittenberger and Morgenbesser to deal with infinite systems of f...
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Answering a question of Kolaitis and Kopparty, we show that, for given integer q > 1 and pairwise nonisomorphic connected graphs G1, . . . , Gk, if p = p(n) is such that Pr(Gn,p ⊇ Gi) → 1 ∀i, then, with ξi the number of copies of Gi in Gn,p, (ξ1, . . . , ξk) is asymptotically uniformly distributed on Z k q .
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We study the problem of testing for community structure in networks using relations between the observed frequencies of small subgraphs. We propose a simple test for the existence of communities based only on the frequencies of three-node subgraphs. The test statistic is shown to be asymptotically normal under a null assumption of no community structure, and to have power approaching one under ...
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We present techniques for maintaining subgraph frequencies in a dynamic graph, using data structures that are parameterized in terms of h, the h-index of the graph. Our methods extend previous results of Eppstein and Spiro for maintaining statistics for undirected subgraphs of size three to directed subgraphs and to subgraphs of size four. For the directed case, we provide a data structure to m...
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2018
ISSN: 0024-6107,1469-7750
DOI: 10.1112/jlms.12192