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

open allclose all

Basic Examples(1)

Correlation similarity between two vertices in a graph:

Scope(7)

VertexCorrelationSimilarity works with undirected graphs:

Directed graphs:

Weighted graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

VertexCorrelationSimilarity works with large graphs:

Properties & Relations(3)

Use CorrelationDistance to compute the correlation similarity of a graph:

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

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

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_2024_vertexcorrelationsimilarity, author="Wolfram Research", title="{VertexCorrelationSimilarity}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/VertexCorrelationSimilarity.html}", note=[Accessed: 13-June-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_vertexcorrelationsimilarity, organization={Wolfram Research}, title={VertexCorrelationSimilarity}, year={2015}, url={https://reference.wolfram.com/language/ref/VertexCorrelationSimilarity.html}, note=[Accessed: 13-June-2024 ]}