# 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:

## 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: