# Random graphs with general degree distributions

# Random graphs with general degree distributions

This chapter describes more sophisticated random graph models that mimic networks with arbitrary degree distributions

The previous chapter looked at the classic random graph model, in which pairs of vertices are connected at random with uniform probabilities. Although this model has proved tremendously useful as a source of insight into the structure of networks, it also has a number of serious shortcomings. Chief among these is its degree distribution, which follows the Poisson distribution which is quite different from the degree distributions seen in most real-world networks. This chapter shows how to create more sophisticated random graph models, which incorporate arbitrary degree distributions and yet are still exactly solvable for many of their properties in the limit of large network size. The fundamental mathematical tool used to derive the results of this chapter is the probability generating function. Exercises are provided at the end of the chapter.

*Keywords:*
random graphs, network models, probability generating function, random graph models, Poisson distribution

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