Clustered Power-Law Networks

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 power-law 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.



  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


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
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+