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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
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Basic Examples  
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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:

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

Scope  (6)

VertexJaccardSimilarity works with undirected graphs:

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

Directed graphs:

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

Multigraphs:

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

Mixed graphs:

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

Use rules to specify the graph:

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

VertexJaccardSimilarity works with large graphs:

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

Properties & Relations  (3)

Use JaccardDissimilarity to compute the Jaccard similarity of a graph:

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

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

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

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

Wolfram Language code: VertexJaccardSimilarity[[image], 1, 2]
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_2026_vertexjaccardsimilarity, author="Wolfram Research", title="{VertexJaccardSimilarity}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/VertexJaccardSimilarity.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_vertexjaccardsimilarity, organization={Wolfram Research}, title={VertexJaccardSimilarity}, year={2015}, url={https://reference.wolfram.com/language/ref/VertexJaccardSimilarity.html}, note=[Accessed: 13-June-2026]}