represents a Barabasi–Albert graph distribution for n-vertex graphs where a new vertex with k edges is added at each step.
- 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.
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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: