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VertexCorrelationSimilarity[g,u,v]

gives the correlation similarity between vertices u and v of the graph g.

VertexCorrelationSimilarity[{vw,…},…]

uses rules vw to specify the graph g.

Details
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Basic Examples  
Scope  
Properties & Relations  
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VertexCorrelationSimilarity

VertexCorrelationSimilarity[g,u,v]

gives the correlation similarity between vertices u and v of the graph g.

VertexCorrelationSimilarity[{vw,…},…]

uses rules vw to specify the graph g.

Details

  • The vertex correlation similarity is also known as Pearson correlation coefficients.
  • VertexCorrelationSimilarity works with undirected graphs, directed graphs, weighted graphs, multigraphs, and mixed graphs.

Examples

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Basic Examples  (1)

Correlation similarity between two vertices in a graph:

Wolfram Language code: VertexCorrelationSimilarity[[image], 1, 2]

Scope  (7)

VertexCorrelationSimilarity works with undirected graphs:

Wolfram Language code: VertexCorrelationSimilarity[[image], 1, 4]

Directed graphs:

Wolfram Language code: VertexCorrelationSimilarity[[image], 1, 4]

Weighted graphs:

Wolfram Language code: VertexCorrelationSimilarity[[image], 1, 4]

Multigraphs:

Wolfram Language code: VertexCorrelationSimilarity[[image], 1, 4]

Mixed graphs:

Wolfram Language code: VertexCorrelationSimilarity[[image], 1, 3]

Use rules to specify the graph:

Wolfram Language code: VertexCorrelationSimilarity[{1 -> 2, 2 -> 3, 3 -> 1, 3 -> 4}, 1, 4]

VertexCorrelationSimilarity works with large graphs:

Wolfram Language code: g = ExampleData[{"NetworkGraph", "Internet"}];
Wolfram Language code: VertexCorrelationSimilarity[g, 1, 26]//N//Timing

Properties & Relations  (3)

Use CorrelationDistance to compute the correlation similarity of a graph:

Wolfram Language code: g = [image];
Wolfram Language code: m = Normal[AdjacencyMatrix[g]];
Wolfram Language code: {1 - CorrelationDistance[m[[1]], m[[7]]], VertexCorrelationSimilarity[g, 1, 7]}

The cosine similarity between two vertices is equal to zero if one of them has degree zero:

Wolfram Language code: VertexCorrelationSimilarity[[image], 1, 4]

The correlation similarity between two vertices is equal to one if they have the same neighbors:

Wolfram Language code: VertexCorrelationSimilarity[[image], 1, 2]
Wolfram Research (2012), VertexCorrelationSimilarity, Wolfram Language function, https://reference.wolfram.com/language/ref/VertexCorrelationSimilarity.html (updated 2015).

Text

Wolfram Research (2012), VertexCorrelationSimilarity, Wolfram Language function, https://reference.wolfram.com/language/ref/VertexCorrelationSimilarity.html (updated 2015).

CMS

Wolfram Language. 2012. "VertexCorrelationSimilarity." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/VertexCorrelationSimilarity.html.

APA

Wolfram Language. (2012). VertexCorrelationSimilarity. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/VertexCorrelationSimilarity.html

BibTeX

@misc{reference.wolfram_2026_vertexcorrelationsimilarity, author="Wolfram Research", title="{VertexCorrelationSimilarity}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/VertexCorrelationSimilarity.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_vertexcorrelationsimilarity, organization={Wolfram Research}, title={VertexCorrelationSimilarity}, year={2015}, url={https://reference.wolfram.com/language/ref/VertexCorrelationSimilarity.html}, note=[Accessed: 13-June-2026]}