# VertexCosineSimilarity

VertexCosineSimilarity[g,u,v]

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

VertexCosineSimilarity[{vw,},]

uses rules vw to specify the graph g.

# Details

• The vertex cosine similarity is also known as Salton similarity.
• The vertex cosine similarity is the number of common neighbors of u and v divided by the geometric mean of their degrees.
• VertexCosineSimilarity works with undirected graphs, directed graphs, weighted graphs, multigraphs, and mixed graphs.

# Examples

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## Basic Examples(1)

Cosine similarity between two vertices in a graph:

## Scope(7)

VertexCosineSimilarity works with undirected graphs:

Directed graphs:

Weighted graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

VertexCosineSimilarity works with large graphs:

## Properties & Relations(3)

Use CosineDistance to compute the cosine similarity of a graph:

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

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

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2023_vertexcosinesimilarity, author="Wolfram Research", title="{VertexCosineSimilarity}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/VertexCosineSimilarity.html}", note=[Accessed: 01-October-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2023_vertexcosinesimilarity, organization={Wolfram Research}, title={VertexCosineSimilarity}, year={2015}, url={https://reference.wolfram.com/language/ref/VertexCosineSimilarity.html}, note=[Accessed: 01-October-2023 ]}