Random Graphs and Network Models

One of the most important concepts in network analysis is to understand the structure of a given graph with respect to a set of suitably randomized graphs, a so-called random graph model. Structures which are found to be significantly different from those expected in the random graph model require a new random graph model which exemplifies how the structure might emerge in the complex network. In this chapter the most common random graph models are introduced: the classic Erdős-Renyi model, the small-world model by Watts and Strogatz, and the preferential attachment model by Barabasi and Albert.

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