Part III Weighted Graphs. Introduction -- Basic tools -- Part II: Erdos-Renyi-Gilbert Model -- Uniform and Binomial Random Graphs -- Evolution -- Vertex Degrees -- Connectivity -- Small Subgraphs -- Large Subgraphs -- Extreme Characteristics -- Part III Modeling Complex Networks -- Inhomogeneous Graphs -- Small World -- Network Processes -- Intersection Graphs -- Weighted Graphs.
Summary:
Networks surround us, from social networks to protein-protein interaction networks within the cells of our bodies. The theory of random graphs provides a necessary framework for understanding their structure and development. This text provides an accessible introduction to this rapidly expanding subject. It covers all the basic features of random graphs - component structure, matchings and Hamilton cycles, connectivity and chromatic number - before discussing models of real-world networks, including intersection graphs, preferential attachment graphs and small-world models. Based on the authors' own teaching experience, it can be used as a textbook for a one-semester course on random graphs and networks at advanced undergraduate or graduate level. The text includes numerous exercises, with a particular focus on developing students' skills in asymptotic analysis. More challenging problems are accompanied by hints or suggestions for further reading.
This resource is supported by the Institute of Museum and Library Services under the provisions of the Library Services and Technology Act as administered by State Library of Iowa.