constraint              package:igraph              R Documentation

_B_u_r_t'_s _c_o_n_s_t_r_a_i_n_t

_D_e_s_c_r_i_p_t_i_o_n:

     Given a graph, 'constraint' calculates Burt's constraint for each
     vertex.

_U_s_a_g_e:

     constraint(graph, nodes=V(graph), weights=NULL)

_A_r_g_u_m_e_n_t_s:

   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 'NULL' and there is a
          'weight' edge attribute this is used. If there is no such
          edge attribute all edges will have the same weight.

_D_e_t_a_i_l_s:

     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,q] p[q,j])^2, q in V[i], q != i,j ), j in V[], 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.

_V_a_l_u_e:

     A numeric vector of constraint scores

_A_u_t_h_o_r(_s):

     Jeroen Bruggeman j.p.bruggeman@uva.nl and Gabor Csardi
     csardi@rmki.kfki.hu

_R_e_f_e_r_e_n_c_e_s:

     Burt, R.S. (2004). Structural holes and good ideas. _American
     Journal of Sociology_ 110, 349-399.

_E_x_a_m_p_l_e_s:

     g <- erdos.renyi.game(20, 5/20)
     constraint(g)

