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VertexCosineSimilarity
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VertexCosineSimilarity

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

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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)Summary of the most common use cases

Cosine similarity between two vertices in a graph:

In[1]:=1
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https://wolfram.com/xid/0k2yyinvid6qgzybpsy-ympua
Out[1]=1

Scope  (7)Survey of the scope of standard use cases

VertexCosineSimilarity works with undirected graphs:

In[1]:=1
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https://wolfram.com/xid/0k2yyinvid6qgzybpsy-zv6lj
Out[1]=1

Directed graphs:

In[1]:=1
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https://wolfram.com/xid/0k2yyinvid6qgzybpsy-jxhjg5
Out[1]=1

Weighted graphs:

In[1]:=1
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https://wolfram.com/xid/0k2yyinvid6qgzybpsy-g83u6g
Out[1]=1

Multigraphs:

In[1]:=1
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https://wolfram.com/xid/0k2yyinvid6qgzybpsy-15kl6n
Out[1]=1

Mixed graphs:

In[1]:=1
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https://wolfram.com/xid/0k2yyinvid6qgzybpsy-dkxgru
Out[1]=1

Use rules to specify the graph:

In[1]:=1
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https://wolfram.com/xid/0k2yyinvid6qgzybpsy-bndh30
Out[1]=1

VertexCosineSimilarity works with large graphs:

In[1]:=1
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https://wolfram.com/xid/0k2yyinvid6qgzybpsy-gw1usj
In[2]:=2
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https://wolfram.com/xid/0k2yyinvid6qgzybpsy-h0c2nf
Out[2]=2

Properties & Relations  (3)Properties of the function, and connections to other functions

Use CosineDistance to compute the cosine similarity of a graph:

In[2]:=2
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https://wolfram.com/xid/0k2yyinvid6qgzybpsy-mrgwsi
In[3]:=3
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https://wolfram.com/xid/0k2yyinvid6qgzybpsy-gt4ar2
In[4]:=4
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https://wolfram.com/xid/0k2yyinvid6qgzybpsy-fn267z
Out[4]=4

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

In[1]:=1
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https://wolfram.com/xid/0k2yyinvid6qgzybpsy-b59h1d
Out[1]=1

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

In[1]:=1
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https://wolfram.com/xid/0k2yyinvid6qgzybpsy-f6tk9t
Out[1]=1
Wolfram Research (2012), VertexCosineSimilarity, Wolfram Language function, https://reference.wolfram.com/language/ref/VertexCosineSimilarity.html (updated 2015).
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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).

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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.

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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

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

BibTeX

@misc{reference.wolfram_2025_vertexcosinesimilarity, author="Wolfram Research", title="{VertexCosineSimilarity}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/VertexCosineSimilarity.html}", note=[Accessed: 16-April-2025 ]}

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@misc{reference.wolfram_2025_vertexcosinesimilarity, author="Wolfram Research", title="{VertexCosineSimilarity}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/VertexCosineSimilarity.html}", note=[Accessed: 16-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_vertexcosinesimilarity, organization={Wolfram Research}, title={VertexCosineSimilarity}, year={2015}, url={https://reference.wolfram.com/language/ref/VertexCosineSimilarity.html}, note=[Accessed: 16-April-2025 ]}

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@online{reference.wolfram_2025_vertexcosinesimilarity, organization={Wolfram Research}, title={VertexCosineSimilarity}, year={2015}, url={https://reference.wolfram.com/language/ref/VertexCosineSimilarity.html}, note=[Accessed: 16-April-2025 ]}