represents a Barabasi–Albert graph distribution for n-vertex graphs where a new vertex with k edges is added at each step.
- BarabasiAlbertGraphDistribution is also known as scale-free graph distribution.
- The BarabasiAlbertGraphDistribution is constructed starting from CycleGraph, and a vertex with k edges is added at each step. The k edges are attached to vertices at random, following a distribution proportional to the vertex degree.
- BarabasiAlbertGraphDistribution can be used with such functions as RandomGraph and GraphPropertyDistribution.
Examplesopen allclose all
Basic Examples (2)
The internet at the level of autonomous systems can be modeled with BarabasiAlbertGraphDistribution:
A social network with 400 people and prominent hubs is modeled with BarabasiAlbertGraphDistribution. Find the expected number of ties separating a person at the hub from the most remote person in the network:
Properties & Relations (5)
The distribution can be approximated by ZipfDistribution:
In BarabasiAlbertGraphDistribution[n,k], there is a maximum clique of size k+1:
Wolfram Research (2010), BarabasiAlbertGraphDistribution, Wolfram Language function, https://reference.wolfram.com/language/ref/BarabasiAlbertGraphDistribution.html.
Wolfram Language. 2010. "BarabasiAlbertGraphDistribution." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BarabasiAlbertGraphDistribution.html.
Wolfram Language. (2010). BarabasiAlbertGraphDistribution. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BarabasiAlbertGraphDistribution.html