Given a graph, constraint calculates Burt's constraint for
each vertex.
Usage
constraint(graph, nodes=V(graph))
Arguments
graph
A graph object, the input graph.
nodes
The vertices for which the constraint will be
calculated. Defaults to all vertices.
Value
A numeric vector of constraint scores
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.