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Summary: OPERATIONS RESEARCH AND MANAGEMENT
SCIENCE HANDBOOK
Editor: A. Ravi Ravindran
The Pennsylvania State University
December 1, 2006
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Contents
11 Complexity and Large-scale Networks 1
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
11.2 Statistical properties of complex networks . . . . . . . . . . . . . . . . . . . 8
11.2.1 Average path length and the small-world effect . . . . . . . . . . . . . 8
11.2.2 Clustering coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
11.2.3 Degree distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
11.2.4 Betweenness centrality . . . . . . . . . . . . . . . . . . . . . . . . . . 12
11.2.5 Modularity and community structures . . . . . . . . . . . . . . . . . 13
11.2.6 Network resilience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
11.3 Modeling of complex networks . . . . . . . . . . . . . . . . . . . . . . . . . . 16
11.3.1 Random graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
11.3.2 Small-world networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
11.3.3 Scale-free networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
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