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BUILT-IN MATHEMATICA SYMBOL

BarabasiAlbertGraphDistribution

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.

Generate a Barabasi-Albert graph with 30 vertices and 2 edges added at each step:

Generate several graphs:

Generate a Barabasi-Albert graph with 30 vertices and 2 edges added at each step:

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Generate several graphs:

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Do a simple implementation of a Barabasi-Albert graph generation scheme:

Compare degree distributions from above with the built-in function:

The mean graph distance increases slowly for a Barabasi-Albert graph:

The graph diameter increases slowly for a Barabasi-Albert graph:

The vertex degree distribution for BarabasiAlbertGraphDistribution is heavy tailed:

The degree distribution is heavy tailed, so logarithmic scales make it clearer:

There is great variation in the vertex degree:

BarabasiAlbertGraphDistribution cannot generate directed graphs:

Random colored vertices: