# Clustered Power-Law Networks

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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 connects with an existing node is proportional to the fraction of edges already incoming to . 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 (), a new node connects to a random selection of the neighbors of the node to which last connected. This Demonstration permits the user to construct an undirected clustered powerÃ¢Â€Âlaw network by letting them select , 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.

Contributed by: Seth J. Chandler (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

P. Holme and B.J. Kim, "Growing Scale-Free Networks with Tunable Clustering," *Physical Review* [Online Archive], 65(2), 2002 pp. 1-4. http://prola.aps.org/abstract/PRE/v65/i2/e026107.

Snapshot 1: a high number of edges

Snapshot 2: a high proportion of clustered nodes

## Permanent Citation

"Clustered Power-Law Networks"

http://demonstrations.wolfram.com/ClusteredPowerLawNetworks/

Wolfram Demonstrations Project

Published: March 7 2011