# VertexJaccardSimilarity

VertexJaccardSimilarity[g,u,v]

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

VertexJaccardSimilarity[{vw,},]

uses rules vw to specify the graph g.

# Details

• The vertex Jaccard similarity is also known as Jaccard index and Jaccard similarity coefficient.
• The vertex Jaccard similarity between u and v is the number of common neighbors of u and v divided by the number of vertices that are neighbors of u or v.
• VertexJaccardSimilarity works with undirected graphs, directed graphs, multigraphs, and mixed graphs.

# Examples

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## Basic Examples(1)

Jaccard similarity between two vertices in a graph:

## Scope(6)

VertexJaccardSimilarity works with undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

VertexJaccardSimilarity works with large graphs:

## Properties & Relations(3)

Use JaccardDissimilarity to compute the Jaccard similarity of a graph:

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

The Jaccard similarity between two vertices is equal to 1 if they have the same neighbors:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_vertexjaccardsimilarity, author="Wolfram Research", title="{VertexJaccardSimilarity}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/VertexJaccardSimilarity.html}", note=[Accessed: 17-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_vertexjaccardsimilarity, organization={Wolfram Research}, title={VertexJaccardSimilarity}, year={2015}, url={https://reference.wolfram.com/language/ref/VertexJaccardSimilarity.html}, note=[Accessed: 17-July-2024 ]}