# count_triangles

0th

Percentile

##### Find triangles in graphs

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

Keywords
graphs
##### Usage
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.
##### 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.

##### Value

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

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

transitivity

##### Aliases
• count_triangles
• triangles
##### Examples
## A small graph
kite <- make_graph("Krackhardt_Kite")
plot(kite)
matrix(triangles(kite), nrow=3)

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

## Always true
sum(count_triangles(kite)) == length(triangles(kite))

## Should match, local transitivity is the
## number of adjacent triangles divided by the number
count_triangles(kite) / (degree(kite) * (degree(kite)-1)/2)