PriceGraphDistribution

PriceGraphDistribution[n,k,a]

represents a de Solla Price graph distribution for n-vertex graphs where a new vertex with k edges is added at each step, using attractiveness parameter a.

Details and Options

Examples

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Basic Examples  (2)

Generate a pseudorandom graph:

In-degree distribution:

Probability density function:

Scope  (4)

Generate simple directed graphs:

Simple undirected graphs:

Generate a set of pseudorandom graphs:

Compute probabilities and statistical properties:

Options  (2)

DirectedEdges  (2)

By default, the Price graph is a directed graph:

With the setting DirectedEdges->False, undirected Price graphs are generated:

Applications  (2)

A citation network can be modeled with PriceGraphDistribution:

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

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

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

Properties & Relations  (4)

Distribution of the number of vertices:

Distribution of the number of edges:

In-degree distribution:

The distribution can be approximated by ZipfDistribution:

The degree distribution follows a power-law:

Use RandomSample to simulate PriceGraphDistribution:

Neat Examples  (1)

Randomly colored vertices:

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

Text

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

BibTeX

@misc{reference.wolfram_2020_pricegraphdistribution, author="Wolfram Research", title="{PriceGraphDistribution}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/PriceGraphDistribution.html}", note=[Accessed: 01-December-2020 ]}

BibLaTeX

@online{reference.wolfram_2020_pricegraphdistribution, organization={Wolfram Research}, title={PriceGraphDistribution}, year={2010}, url={https://reference.wolfram.com/language/ref/PriceGraphDistribution.html}, note=[Accessed: 01-December-2020 ]}

CMS

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

APA

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