BarabasiAlbertGraphDistribution

BarabasiAlbertGraphDistribution[n,k]

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

Details

Examples

open allclose all

Basic Examples  (2)

Generate a pseudorandom graph:

Degree distribution:

Probability density function:

Scope  (3)

Generate simple undirected graphs:

Generate a set of pseudorandom graphs:

Compute probabilities and statistical properties:

Applications  (3)

The internet at the level of autonomous systems can be modeled with BarabasiAlbertGraphDistribution:

The model captures the power-law nature of the empirical degree distribution:

The model has a lower clustering coefficient:

Use the BarabasiAlbert graph distribution as a model of the Western States Power Grid network:

The model captures the power-law nature of the empirical degree distribution:

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)

Distribution of the number of vertices:

Distribution of the number of edges:

Degree distribution:

The distribution can be approximated by ZipfDistribution:

The degree distribution follows a power law:

Use RandomSample to simulate a BarabasiAlbertGraphDistribution:

Pseudorandom graphs:

In BarabasiAlbertGraphDistribution[n,k], there is a maximum clique of size k+1:

Neat Examples  (1)

Randomly colored vertices:

Introduced in 2010
 (8.0)