triangle-ergmTerm {ergm}

Triangles

Description

By default, this term adds one statistic to the model equal to the number of triangles in the network. For an undirected network, a triangle is defined to be any set \{(i,j), (j,k), (k,i)\} of three edges. For a directed network, a triangle is defined as any set of three edges (i{\rightarrow}j) and (j{\rightarrow}k) and either (k{\rightarrow}i) or (k{\leftarrow}i) . The former case is called a "transitive triple" and the latter is called a "cyclic triple", so in the case of a directed network, triangle equals ttriple plus ctriple — thus at most two of these three terms can be in a model.

Usage

# binary: triangle(attr=NULL, diff=FALSE, levels=NULL)

# binary: triangles(attr=NULL, diff=FALSE, levels=NULL)

Arguments

attr, diff

quantitative attribute (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.) If attr is specified and diff is FALSE , then the count is restricted to those triples of nodes with equal values of the vertex attribute specified by attr . If attr is specified and diff is TRUE , then one statistic is added for each value of attr , equal to the number of triangles where all three nodes have that value of the attribute.

levels

add one statistic for each value specified if diff is TRUE. (See Specifying Vertex attributes and Levels (?nodal_attributes) for details.)

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, directed, frequently-used, triad-related, undirected, binary