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
- The PriceGraphDistribution is constructed starting from a graph with a single vertex and at each step adding a vertex with k edges. The k edges are attached to vertices at random with weights qi+a, where qi is the in-degree of vertex i.
- PriceGraphDistribution can be used with such functions as RandomGraph and GraphPropertyDistribution.
Examplesopen allclose all
Basic Examples (2)
By default, the Price graph is a directed graph:
With the setting DirectedEdges->False, undirected Price graphs are generated:
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:
The distribution can be approximated by ZipfDistribution:
The degree distribution follows a power-law:
Use RandomSample to simulate PriceGraphDistribution:
Wolfram Research (2010), PriceGraphDistribution, Wolfram Language function, https://reference.wolfram.com/language/ref/PriceGraphDistribution.html.
Wolfram Language. 2010. "PriceGraphDistribution." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PriceGraphDistribution.html.
Wolfram Language. (2010). PriceGraphDistribution. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PriceGraphDistribution.html