These functions calculates similarity scores for vertices based on their connection patterns.

## Usage

similarity(
graph,
vids = V(graph),
mode = c("all", "out", "in", "total"),
loops = FALSE,
method = c("jaccard", "dice", "invlogweighted")
)

## Arguments

graph

The input graph.

vids

The vertex ids for which the similarity is calculated.

mode

The type of neighboring vertices to use for the calculation, possible values: ‘out’, ‘in’, ‘all’.

loops

Whether to include vertices themselves in the neighbor sets.

method

The method to use.

## Value

A length(vids) by length(vids) numeric matrix containing the similarity scores. This argument is ignored by the invlogweighted method.

## Details

The Jaccard similarity coefficient of two vertices is the number of common neighbors divided by the number of vertices that are neighbors of at least one of the two vertices being considered. The jaccard method calculates the pairwise Jaccard similarities for some (or all) of the vertices.

The Dice similarity coefficient of two vertices is twice the number of common neighbors divided by the sum of the degrees of the vertices. Methof dice calculates the pairwise Dice similarities for some (or all) of the vertices.

The inverse log-weighted similarity of two vertices is the number of their common neighbors, weighted by the inverse logarithm of their degrees. It is based on the assumption that two vertices should be considered more similar if they share a low-degree common neighbor, since high-degree common neighbors are more likely to appear even by pure chance. Isolated vertices will have zero similarity to any other vertex. Self-similarities are not calculated. See the following paper for more details: Lada A. Adamic and Eytan Adar: Friends and neighbors on the Web. Social Networks, 25(3):211-230, 2003.

## References

Lada A. Adamic and Eytan Adar: Friends and neighbors on the Web. Social Networks, 25(3):211-230, 2003.

Other cocitation: cocitation()

## Author

Tamas Nepusz ntamas@gmail.com and Gabor Csardi csardi.gabor@gmail.com for the manual page.

## Examples


g <- make_ring(5)
similarity(g, method = "dice")
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]  1.0  0.0  0.5  0.5  0.0
#> [2,]  0.0  1.0  0.0  0.5  0.5
#> [3,]  0.5  0.0  1.0  0.0  0.5
#> [4,]  0.5  0.5  0.0  1.0  0.0
#> [5,]  0.0  0.5  0.5  0.0  1.0
similarity(g, method = "jaccard")
#>           [,1]      [,2]      [,3]      [,4]      [,5]
#> [1,] 1.0000000 0.0000000 0.3333333 0.3333333 0.0000000
#> [2,] 0.0000000 1.0000000 0.0000000 0.3333333 0.3333333
#> [3,] 0.3333333 0.0000000 1.0000000 0.0000000 0.3333333
#> [4,] 0.3333333 0.3333333 0.0000000 1.0000000 0.0000000
#> [5,] 0.0000000 0.3333333 0.3333333 0.0000000 1.0000000