Find triangles in graphs

Count how many triangles a vertex is part of, in a graph, or just list the triangles of a graph.

Usage

triangles(graph)

count_triangles(graph, vids = V(graph))

Arguments

graph: The input graph. It might be directed, but edge directions are ignored.
vids: The vertices to query, all of them by default. This might be a vector of numeric ids, or a character vector of symbolic vertex names for named graphs.

Value

For triangles() a numeric vector of vertex ids, the first three vertices belong to the first triangle found, etc.

For count_triangles() a numeric vector, the number of triangles for all vertices queried.

Details

triangles() lists all triangles of a graph. For efficiency, all triangles are returned in a single vector. The first three vertices belong to the first triangle, etc.

count_triangles() counts how many triangles a vertex is part of.

Author

Gabor Csardi csardi.gabor@gmail.com

igraph_list_triangles(), igraph_adjacent_triangles().

Examples


## A small graph
kite <- make_graph("Krackhardt_Kite")
plot(kite)

matrix(triangles(kite), nrow = 3)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11]
#> [1,]    4    4    4    4    4    4    4    4    6     6     7
#> [2,]    1    1    2    6    6    6    7    7    1     7     2
#> [3,]    2    3    5    1    3    7    2    5    3     8     5

## Adjacenct triangles
atri <- count_triangles(kite)
plot(kite, vertex.label = atri)


## Always true
sum(count_triangles(kite)) == length(triangles(kite))
#> [1] TRUE

## Should match, local transitivity is the
## number of adjacent triangles divided by the number
## of adjacency triples
transitivity(kite, type = "local")
#>  [1] 0.6666667 0.6666667 1.0000000 0.5333333 1.0000000 0.5000000 0.5000000
#>  [8] 0.3333333 0.0000000       NaN
count_triangles(kite) / (degree(kite) * (degree(kite) - 1) / 2)
#>  [1] 0.6666667 0.6666667 1.0000000 0.5333333 1.0000000 0.5000000 0.5000000
#>  [8] 0.3333333 0.0000000       NaN