reachability               package:sna               R Documentation

_F_i_n_d _t_h_e _R_e_a_c_h_a_b_i_l_i_t_y _M_a_t_r_i_x _o_f _a _G_r_a_p_h

_D_e_s_c_r_i_p_t_i_o_n:

     'reachability' takes a (possibly directed) graph as input,
     producing the associated reachability matrix.

_U_s_a_g_e:

     reachability(dat, geodist.precomp=NULL)

_A_r_g_u_m_e_n_t_s:

     dat: A graph adjacency matrix (directed or otherwise) 

geodist.precomp: Optionally, a precomputed 'geodist' object 

_D_e_t_a_i_l_s:

     For a digraph G=(V,E) with vertices i and j, let P_ij represent a
     directed ij path.  Then the graph


           R = ( V(G), { (i,j): i,j in V(G), P_ij in G } )


     is said to be the _reachability graph_ of G, and the adjacency
     matrix of R is said to be G's _reachability matrix_.  (Note that
     when G is undirected, we simply take each undirected edge to be
     bidirectional.)  Vertices which are adjacent in the reachability
     graph are connected by one or more directed paths in the original
     graph; thus, structural equivalence classes in the reachability
     graph are synonymous with strongly connected components in the
     original structure.

     Bear in mind that - as with all matters involving connectedness -
     reachability is strongly related to size and density.  Since, for
     any given density, almost all structures of sufficiently large
     size are connected, reachability graphs associated with large
     structures will generally be complete.  Measures based on the
     reachability graph, then, will tend to become degenerate in the
     large |V(G)| limit (assuming constant positive density).

_V_a_l_u_e:

     A reachability matrix

_A_u_t_h_o_r(_s):

     Carter T. Butts buttsc@uci.edu

_R_e_f_e_r_e_n_c_e_s:

     Wasserman, S., and Faust, K.  (1994).  ``Social Network Analysis:
     Methods and Applications.''  Cambridge: Cambridge University
     Press.

_S_e_e _A_l_s_o:

     'geodist'

_E_x_a_m_p_l_e_s:

     #Find the reachability matrix for a sparse random graph
     g<-rgraph(10,tprob=0.15)
     rg<-reachability(g)
     g  #Compare the two structures
     rg

     #Compare to the output of geodist
     all(rg==(geodist(g)$counts>0))

