Clustered Power-Law Networks

probability of triad formation

0.5

number of edges

50

bounds on distribution of edges from each node

random seed

large format

A network in which the degree distribution follows a power law can be constructed through a process of preferential attachment in which the probability that a new node

Y

connects with an existing node

X

is proportional to the fraction of edges already incoming to

X

. As shown by Holme & Kim in 2002, one can construct a network in which the degree distribution follows a power law but also exhibits "clustering" by requiring that, in some fraction of cases (

p

), a new node

Y

connects to a random selection of the neighbors of the node to which

Y

last connected. This Demonstration permits the user to construct an undirected clustered power-law network by letting them select

p

, the number of edges to be created, and the bounds on the uniform distribution that determines the number of edges that will emerge from each new node.