View source: R/structural.properties.R

constraint | 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 (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)

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