منابع مشابه
Edge-exchangeable graphs and sparsity
A known failing of many popular random graph models is that the Aldous–Hoover Theorem guarantees these graphs are dense with probability one; that is, the number of edges grows quadratically with the number of nodes. This behavior is considered unrealistic in observed graphs. We define a notion of edge exchangeability for random graphs in contrast to the established notion of infinite exchangea...
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We consider the distribution of cycle counts in a random regular graph, which is closely linked to the graph’s spectral properties. We broaden the asymptotic regime in which the cycle counts are known to be approximately Poisson, and we give an explicit bound in total variation distance for the approximation. Using this result, we calculate limiting distributions of linear eigenvalue statistics...
متن کاملGraph Limits and Exchangeable Random Graphs
We develop a clear connection between deFinetti’s theorem for exchangeable arrays (work of Aldous–Hoover–Kallenberg) and the emerging area of graph limits (work of Lovász and many coauthors). Along the way, we translate the graph theory into more classical prob-
متن کاملSparse graphs using exchangeable random measures
Statistical network modelling has focused on representing the graph as a discrete structure, namely the adjacency matrix. When assuming exchangeability of this array-which can aid in modelling, computations and theoretical analysis-the Aldous-Hoover theorem informs us that the graph is necessarily either dense or empty. We instead consider representing the graph as an exchangeable random measur...
متن کاملThe Class of Random Graphs Arising from Exchangeable Random Measures
We introduce a class of random graphs that we argue meets many of the desiderata one would demand of a model to serve as the foundation for a statistical analysis of real-world networks. The class of random graphs is defined by a probabilistic symmetry: invariance of the distribution of each graph to an arbitrary relabelings of its vertices. In particular, following Caron and Fox, we interpret ...
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ژورنال
عنوان ژورنال: Journal of Statistical Physics
سال: 2017
ISSN: 0022-4715,1572-9613
DOI: 10.1007/s10955-017-1832-9