On the Limiting Distribution of a Graph Scan Statistic
| Autor: | Andrey Rukhin, Carey E. Priebe |
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| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | Communications in Statistics - Theory and Methods. 41:1151-1170 |
| ISSN: | 1532-415X 0361-0926 |
| DOI: | 10.1080/03610926.2010.533237 |
| Popis: | Let p ∈ (0, 1) and let n ∈ ℕ. Moreover, let s ∈ (p, 1], let m = m(n) be a positive, integer-valued function of n with for some positive integer k. We define ER(n, p) to be the random graph model on n vertices where each edge is independently included in the graph with probability p. We also define κ(n, p, m, s) to be the random graph model on n vertices where edges are included independently; however, there is a fixed subset of m vertices for which each of the edges are included with probability s (and the remaining edges are each included with probability p). Let G = (V, E) denote a graph on n vertices. For any vertex v ∈ V, let N[v] denote the set of neighbors of v along with v itself, and let Ω[v] denote the induced subgraph on this neighborhood of vertices. The aim of this article is to determine the limiting distribution (n → ∞) of the graph scan statistic We prove that is asymptotically Gumbel in both the ER(n, p) and κ(n, p, m, s) random graph models. |
| Databáze: | OpenAIRE |
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