Multiplexing in Networks and Diffusion
Arun G. Chandrasekhar, Vasu Chaudhary, Benjamin Golub, Matthew O. Jackson
TL;DR
This paper develops both a theoretical and empirical lens on multiplex networks, showing that overlapping layers qualitatively alter diffusion dynamics. It introduces a formal model of diffusion across $L$ layers with layer-specific transmission probabilities and a threshold mechanism, deriving when multiplexing dampens simple contagion and produces nuanced, nonmonotonic effects for complex contagion. Empirically, it documents strong inter-layer correlations yet meaningful differences across layers in 143 Indian villages, demonstrates that the advice layer most strongly predicts diffusion, and introduces a backbone index via PCA to capture multiplex structure. Simulations corroborate the theory, revealing that more multiplexing generally reduces diffusion for simple contagion while producing mixed effects for complex contagion depending on infection prevalence. The findings have implications for understanding diffusion of information and norms, and for addressing inequality in access to information across subpopulations.
Abstract
Social and economic networks are often multiplexed, meaning that people are connected by different types of relationships -- such as borrowing goods and giving advice. We make two contributions to the study of multiplexing and the understanding of simple versus complex contagion. On the theoretical side, we introduce a model and theoretical results about diffusion in multiplex networks. We show that multiplexing impedes the spread of simple contagions, such as diseases or basic information that only require one interaction to transmit an infection. We show, however that multiplexing enhances the spread of a complex contagion when infection rates are low, but then impedes complex contagion if infection rates become high. On the empirical side, we document empirical multiplexing patterns in Indian village data. We show that relationships such as socializing, advising, helping, and lending are correlated but distinct, while commonly used proxies for networks based on ethnicity and geography are nearly uncorrelated with actual relationships. We also show that these layers and their overlap affect information diffusion in a field experiment. The advice network is the best predictor of diffusion, but combining layers improves predictions further. Villages with greater overlap between layers -- more multiplexing -- experience less overall diffusion. Finally, we identify differences in multiplexing by gender and connectedness. These have implications for inequality in diffusion-mediated outcomes such as access to information and adherence to norms.