Finding globally optimal macrostructure in multiple relation, mixed-mode social networks
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Authors
Dabkowski, Matthew F.
Fan, Neng
Breiger, Ronald
Issue Date
2020
Type
journal-article
Language
Keywords
Exploratory blockmodeling , Integer programming , Mixed-mode network , Social position , Isomorphism , Structural equivalence
Alternative Title
Abstract
From the outset, computational sociologists have stressed leveraging multiple relations when blockmodeling social networks. Despite this emphasis, the majority of published research over the past 40 years has focused on solving blockmodels for a single relation. When multiple relations exist, a reductionist approach is often employed, where the relations are stacked or aggregated into a single matrix, allowing the researcher to apply single relation, often heuristic, blockmodeling techniques. Accordingly, in this article, we develop an exact procedure for the exploratory blockmodeling of multiple relation, mixed-mode networks. In particular, given (a) [Formula: see text] actors, (b) [Formula: see text] events, (c) an [Formula: see text] binary one-mode network depicting the ties between actors, and (d) an [Formula: see text] binary two-mode network representing the ties between actors and events, we use integer programming to find globally optimal [Formula: see text] image matrices and partitions, where [Formula: see text] and [Formula: see text] represent the number of actor and event positions, respectively. Given the problem’s computational complexity, we also develop an algorithm to generate a minimal set of non-isomorphic image matrices, as well as a complementary, easily accessible heuristic using the network analysis software Pajek. We illustrate these concepts using a simple, hypothetical example, and we apply our techniques to a terrorist network.
Description
Citation
Dabkowski, M. F., Fan, N., & Breiger, R. (2020). Finding globally optimal macrostructure in multiple relation, mixed-mode social networks. Methodological Innovations, 13(3). https://doi.org/10.1177/2059799120961693
Publisher
Methodological Innovations
License
Journal
Volume
Issue
PubMed ID
ISSN
2059-7991
2059-7991
2059-7991