Degree Distribution on a Random Network

An Erdös-Rényi random graph is one chosen at random from all the graphs with a given number of nodes () and edges (). The degree of a vertex in such a graph follows a Poisson distribution with mean . The blue curve in the left plot is a continuous approximation of , where is the cumulative distribution function of a Poisson distribution with parameter . The red dots show the fraction of nodes of a particular graph with degree .