Building stochastic blockmodels

Social and semantic coevolution in knowledge networks

“…In particular, we broadly elaborate upon role and position analysis to exhibit connections between individual configurations and global structures (Freeman, 1989), between qualitative features and algebraic properties as "patterns" or "stylized facts" characterizing the network (Pattison and Wasserman, 1995;Anderson et al, 1992). Instead of detailing the specificities of every sub-community of the network, we will thus adopt a naturalist rather than ethnographic approach by endeavoring at exhibiting systematic and quantitative structural and behavioral patterns (Callon, 2001).…”

Identifying cohesive subgroups

“…Define G 2 to be the likelihood ratio statistic which measures the adequacy of the fit of a given log-linear or logit model to sociometric data (Anderson et al 1992;Fienberg et al 1985;Wang and Wong 1987;Wasserman and Anderson 1987). Anderson and Wasserman argue strongly that G 2 is an excellent choice for a measure of fit of blocks to data, satisfying the characteristics outlined by Carrington et al (1979).…”

“…Recently, Wasserman and Anderson (1987) and Anderson et al (1992) applied the statistical models developed for sociometric data (or directed graphs) to the task of identifying blocks of stochastically equivalent actors. The blocks are different from subgroups in that blocks of actors engage in common patterns of interaction throughout the network, but do not necessarily engage in the direct interactions which occur between the members of cohesive subgroups (Faust and Wasserman 1994).…”

“…The number of reciprocated or symmetric or mutual relationships also is computed from the marginals of x and is represented by m. The parameter p represents the extent of reciprocity in the network, 0 the density of the network, a is the expansiveness of the actors (associated with out-degree, x/+) and /3 is the attractiveness of the actors (associated with in-degree, X+g,). Wasserman and Anderson (1987) and Anderson et al (1992) identify stochastically equivalent actors based on similarities in their as and /3s through visual and standard clustering methods. The approach can be extended by including parameters representing the relationship between members of each block and members of all other blocks, and Snijders and Nowicki (1994) further extend this by employing the EM algorithm and Gibbs sampling to identify maximum likelihood estimates and standard errors of parameters representing between-block exchanges as well as of parameters representing the probabilities of block membership.…”

Stochastic blockmodels and community structure in networks

“…Stochastic blockmodels fall in the general class of random graph models and have a long tradition of study in the social sciences and computer science [1][2][3][4][5]. In the simplest stochastic blockmodel (many more complicated variants are possible), each of n vertices is assigned to one of K blocks, groups, or communities, and undirected edges are placed independently between vertex pairs with probabilities that are a function only of the group memberships of the vertices.…”