Degree Distribution on a Random Network

nodes

50

edges

10

random seed

An Erdös-Rényi random graph is one chosen at random from all the graphs with a given number of nodes (

n

) and edges (

e

). The degree of a vertex in such a graph follows a Poisson distribution with mean

2e/n

. The blue curve in the left plot is a continuous approximation of

1-f(k)

, where

f(k)

is the cumulative distribution function of a Poisson distribution with parameter

λ=2e/n

. The red dots show the fraction of nodes of a particular graph with degree

k

.