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_{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.
A numeric vector of constraint scores
Jeroen Bruggeman (https://sites.google.com/site/jebrug/jeroen-bruggeman-social-science) and Gabor Csardi csardi.gabor@gmail.com
Burt, R.S. (2004). Structural holes and good ideas. American Journal of Sociology 110, 349-399.
g <- sample_gnp(20, 5/20)
constraint(g)