BarabasiAlbertGraphDistribution

BarabasiAlbertGraphDistribution[n,k]

represents a Barabasi–Albert 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 Barabasi–Albert 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:

Wolfram Research (2010), BarabasiAlbertGraphDistribution, Wolfram Language function, https://reference.wolfram.com/language/ref/BarabasiAlbertGraphDistribution.html.

Text

Wolfram Research (2010), BarabasiAlbertGraphDistribution, Wolfram Language function, https://reference.wolfram.com/language/ref/BarabasiAlbertGraphDistribution.html.

CMS

Wolfram Language. 2010. "BarabasiAlbertGraphDistribution." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BarabasiAlbertGraphDistribution.html.

APA

Wolfram Language. (2010). BarabasiAlbertGraphDistribution. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BarabasiAlbertGraphDistribution.html

BibTeX

@misc{reference.wolfram_2024_barabasialbertgraphdistribution, author="Wolfram Research", title="{BarabasiAlbertGraphDistribution}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/BarabasiAlbertGraphDistribution.html}", note=[Accessed: 21-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_barabasialbertgraphdistribution, organization={Wolfram Research}, title={BarabasiAlbertGraphDistribution}, year={2010}, url={https://reference.wolfram.com/language/ref/BarabasiAlbertGraphDistribution.html}, note=[Accessed: 21-December-2024 ]}