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# Every edge is formed with probability p 0 1

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Unformatted text preview: use the notation G (n, p ) to denote the undirected Erd¨s-Renyi o graph. Every edge is formed with probability p ∈ (0, 1) independently of every other edge. Expected degree of a node i is E[di ] = (n − 1)p 13 Networks: Lecture 2 Properties of Networks Properties of Networks While a small network can be visualized directly by its graph (N , g ), larger networks can be more diﬃcult to envision and describe. Therefore, we deﬁne a set of summary statistics or quantitative p erformance measures to describe and compare networks (focus on undirected graphs): Diameter and average path length Clustering Centrality Degree distributions A Simple Random Graph Model—Erd¨s-Renyi model o We use the notation G (n, p ) to denote the undirected Erd¨s-Renyi o graph. Every edge is formed with probability p ∈ (0, 1) independently of every other edge. Expected degree of a node i is E[di ] = (n − 1)p Expected number of edges is E[number of edges] = 13 Networks: Lecture 2 Properties of Networks Properties of Networks While a small network can be visualized d...
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