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
NULLand there is aweightedge attribute this is used. If there is no such edge attribute all edges will have the same weight.
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 (i.e. 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.
See also
Other structural.properties:
bfs(),
component_distribution(),
connect(),
coreness(),
degree(),
dfs(),
distance_table(),
edge_density(),
feedback_arc_set(),
girth(),
is_acyclic(),
is_dag(),
is_matching(),
k_shortest_paths(),
knn(),
reciprocity(),
subcomponent(),
subgraph(),
topo_sort(),
transitivity(),
unfold_tree(),
which_multiple(),
which_mutual()
Author
Jeroen Bruggeman (https://sites.google.com/site/jebrug/jeroen-bruggeman-social-science) and Gabor Csardi csardi.gabor@gmail.com
Examples
g <- sample_gnp(20, 5 / 20)
constraint(g)
#> [1] 0.2000000 0.3644141 0.2176519 0.4253472 0.3258333 0.3333333 0.3203125
#> [8] 1.0000000 0.2331250 0.3676476 0.2266705 0.2351119 0.2500000 0.3333333
#> [15] 0.3009722 0.3703819 0.4223457 0.2794232 0.3000694 0.3333333