A vector, matrix, or list (depending on dat) containing the structure statistics.
Details
Let $G=(V,E)$ be a graph of order $N$, and let $d(i,j)$ be the geodesic distance from vertex $i$ to vertex $j$ in $G$. The "structure statistics" of $G$ are then given by the series $s_0,\ldots,s_{N-1}$, where $s_i = sum(sum(I(d(j,k)<=i, k="" in="" v),="" j="" v)="" n^2$="" and="" $i$="" is="" the="" standard="" indicator="" function.="" intuitively,="" $s_i$="" expected="" fraction="" of="" $g$="" which="" lies="" within="" distance="" i of a randomly chosen vertex. As such, the structure statistics provide an index of global connectivity.
Structure statistics have been of particular importance to biased net theorists, because of the link with Rapoport's original tracing model. They may also be used along with component distributions or connectedness scores as descriptive indices of connectivity at the graph-level.
References
Fararo, T.J. (1981). ``Biased networks and social structure theorems. Part I.'' Social Networks, 3, 137-159.
Fararo, T.J. (1984). ``Biased networks and social structure theorems. Part II.'' Social Networks, 6, 223-258.
Fararo, T.J. and Sunshine, M.H. (1964). ``A study of a biased friendship net.'' Syracuse, NY: Youth Development Center.
#Generate a moderately sparse Bernoulli graphg<-rgraph(100,tp=1.5/99)
#Compute the structure statistics for gss<-structure.statistics(g)
plot(0:99,ss,xlab="Mean Coverage",ylab="Distance")