Unformatted text preview: use the notation G (n, p ) to denote the undirected Erd¨sRenyi
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¨sRenyi model
o
We use the notation G (n, p ) to denote the undirected Erd¨sRenyi
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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 Fall '09
 Acemoglu
 Graph Theory, Graph Theory and Social Networks

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