An Exact Algorithm for Blockmodeling of Two-Mode Network Data

Abstract

We consider problems where relationships between two sets (or modes) of objects are available in the form of a binary matrix with elements of 1 (0) indicating a bond (lack of a bond) between corresponding row and column objects. The goal is to establish a partition of the row objects and, simultaneously, a partition of the column objects to form blocks that consist of either exclusively 1s or exclusively 0s to the greatest extent possible. This two-mode blockmodeling problem arises in several scientific domains. In the social sciences, two-mode blockmodeling is particularly relevant for social network analysis, where the goal is to simultaneously partition a set of individuals and another set of objects (e.g., events they attended, organizations they are affiliated with, etc.). The inherent computational challenge of simultaneously constructing partitions for two distinct sets of objects has fostered a reliance on heuristics for two-mode blockmodeling. We offer an exact algorithm and demonstrate its efficacy in a simulation study. Two applications to real-world networks are also provided.

Keywords:

• branch-and-bound
• exact algorithms
• generalized blockmodeling
• social networks
• two-mode networks

Notes

Note. Inconsistencies is the optimal value of the criterion function. EWFP is the number of equally well-fitting partitions. Time is the total computation time for the branch-and-bound algorithm in seconds for a 2.4 GHz Core 2 Duo processor.

Note. Inconsistencies is the optimal value of the criterion function. EWFP is the number of equally well-fitting partitions. Time is the total computation time for the branch-and-bound algorithm in seconds for a 2.4 GHz Core 2 Duo processor.