Given a graph, constraint calculates Burt's constraint for
each vertex.
Usage
constraint(graph, nodes=V(graph), weights=NULL)
Arguments
graph
A graph object, the input graph.
nodes
The vertices for which the constraint will be
calculated. Defaults to all vertices.
weights
The weights of the edges. If this is NULL and
there is a weight edge attribute this is used. If there is no
such edge attribute all edges will have the same weight.
Value
A numeric vector of constraint scores
concept
Burt's constraint
Details
Burt's constraint is higher if ego has less, or mutually
stronger related (i.e. more redundant) contacts. Burt's measure of
constraint, $C_i$, of vertex $i$'s ego network
$V_i$, is defined for directed and valued graphs,
$$C_i=\sum_{j \in V_i \setminus {i}} (p_{ij}+\sum_{q \in V_i
\setminus {i,j}} p_{iq} p_{qj})^2$$
for a graph of order (ie. number of vertices) $N$, where
proportional tie strengths are defined as
$$p_{ij} = \frac{a_{ij}+a_{ji}}{\sum_{k \in V_i \setminus {i}}(a_{ik}+a_{ki})},$$
$a_{ij}$ are elements of $A$ and the latter being the
graph adjacency matrix. For isolated vertices, constraint is undefined.
References
Burt, R.S. (2004). Structural holes and good ideas. American
Journal of Sociology 110, 349-399.