constraint {igraph} | R Documentation |
Given a graph, constraint
calculates Burt's constraint for
each vertex.
constraint(graph, nodes=V(graph), weights=NULL)
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 |
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( [sum( p[i,j] + p[i,q] p[q,j], q in V[i], q != i,j )]^2, j in V[i], j != i).
for a graph of order (ie. number of vertices) N, where proportional tie strengths are defined as
p[i,j]=(a[i,j]+a[j,i]) / sum(a[i,k]+a[k,i], k in V[i], k != i),
a[i,j]are elements of A and the latter being the graph adjacency matrix. For isolated vertices, constraint is undefined.
A numeric vector of constraint scores
Jeroen Bruggeman j.p.bruggeman@uva.nl and Gabor Csardi csardi.gabor@gmail.com
Burt, R.S. (2004). Structural holes and good ideas. American Journal of Sociology 110, 349-399.
g <- erdos.renyi.game(20, 5/20) constraint(g)