Random Graphs and Networks: A First Course

A rigorous yet accessible introduction to the rapidly expanding subject of random graphs and networks.

Based on the authors' own teaching experience, this text introduces random graphs and networks, covering all the basic features before discussing the growth and structure of real-world networks. It can be used as a textbook for a one-semester course at advanced undergraduate or graduate level.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.