Although network structures shape diffusion and ultimately systemic performance, the underlying dynamics generating different network structures during diffusion are not well understood. To explore these dynamics we present a set of models driven by a single motivation for generalized balance – the inclination to align the attributes of one’s network members with one’s own attributes either by adopting the attributes of network members or by selecting to interact with similar others. Simulations show that the models generate core-periphery network structures for low levels of generalized balance and polarization (modularity) for high levels of generalized balance. Moreover, the more network members influence one another the more the transition from core-periphery to polarization is delayed but then drastic, in the extreme creating a phase transition. Thus, the rate of influence amplifies the attractiveness of a particular state of the system. The results match transitions in scholarly citation networks and terrorist networks.
Kenneth Frank received his Ph.D. in measurement, evaluation and statistical analysis from the School of Education at the University of Chicago in 1993. He is MSU Foundation professor of Sociometrics, professor in Counseling, Educational Psychology and Special Education; Fisheries and Wildlife, and adjunct (by courtesy) in Sociology at Michigan State University. His substantive interests include the study of schools as organizations, social structures of students and teachers and school decision-making, and social capital. His substantive areas are linked to several methodological interests: social network analysis, causal inference and multi-level models. His publications include quantitative methods for representing relations among actors in a social network, robustness indices for sensitivity analysis for causal inferences, and the effects of social capital in schools and other social contexts. Dr. Frank’s current projects include how beginning teachers’ networks affect their response to the Common Core, how schools respond to increases in core curricular requirements, cognitive linkages among aspects of knowledge, the diffusion of knowledge about climate change, and how the decisions about natural resource use in small communities are embedded in social contexts.