Exploring network structures via blockmodeling of the shortest path length matrix

Among the various methods of network analyses, blockmodeling is one of the key approaches to analyzing network structures. It can be applied not only to position analysis of the individual nodes, but also to cohesive subgroup discovery of the whole network. In this paper, we explore network structures via blockmodeling of the shortest path length matrix. First of all, we dichotomize the shortest path length matrix with different thresholds to generate reachability matrices within different steps. Then, through blockmodeling of the reachability matrix within n steps, we can analyze the network based on the cohesive subgroup, n-clique. Furthermore, through blockmodeling of the maximum reachability matrix, we can fit the network properly into the bowtie structure.