Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 VertexDegreeRelativeFrequencies

Source Notebook

Relative frequencies of VertexDegree in a graph

Contributed by: Soutick Saha

ResourceFunction["VertexDegreeRelativeFrequencies"][graph]

returns the relative frequencies of VertexDegree in a graph.

Details

The output is an Association of VertexDegree values and relative frequencies.
The ResourceFunction["VertexDegreeRelativeFrequencies"] of many real world networks follow power law which indicates its scale free nature. ResourceFunction["VertexDegreeRelativeFrequencies"] can be used to easily analyze such networks.

Examples

Basic Examples (2) 

VertexDegreeRelativeFrequencies of "GolombGraph":

In[1]:=
graph = GraphData["GolombGraph"]
Out[1]=
In[2]:=
ResourceFunction["VertexDegreeRelativeFrequencies"][graph]
Out[2]=

VertexDegreeRelativeFrequencies of a Diseasome Network:

In[3]:=
ResourceData["Bipartite Diseasome Network"]
Out[3]=
In[4]:=
ResourceFunction["VertexDegreeRelativeFrequencies"][ ResourceData["Bipartite Diseasome Network"]]
Out[4]=

Neat Examples (1) 

VertexDegreeRelativeFrequencies of the gene co-expression network in a rat brain:

In[5]:=
ListLogLogPlot[ ResourceFunction["VertexDegreeRelativeFrequencies"][ ResourceData["Rat Brain Graph 1"]], AxesLabel -> {"VertexDegree", "Probability"}, ImageSize -> 500]
Out[5]=

Publisher

WolframChemistry

Version History

  • 1.0.0 – 30 October 2024

Source Metadata

  • Citation:
    • Barabási, Albert-László, and Réka Albert. "Emergence of scaling in random networks." science 286.5439 (1999): 509-512.

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