Funded Grants


Cohesion and connectivity: Methods for identifying endemic diffusion in dynamic networks

Many socially relevant phenomena simply fade away unless constantly refreshed: language requires speakers, ideologies need believers, and scams or rumors need gullible participants. Yet in many cases, these phenomena persist despite both large scale population turnover and concerted efforts to propagate alternatives. For example, social cohesion depends on being able to keep alive a set of common shared beliefs and practices within a collective that turns over continuously and/or faces challenges to their belief system. The mechanics of this process pose a deep mystery for network science: in the face of sometimes massive network turnover, how do some beliefs remain stable? Or, put another way, what are the limits to demographic turnover or competing ideologies in social systems? My goal is to identify the dynamic network foundations for sustaining diffusion; diffusion of things like beliefs that require refreshed interaction to remain endemic.

My strategy to solve this problem builds on insights from structural cohesion (Moody & White 2003) and the limiting effects of relational timing on diffusion (Moody 2002, Kontoleon et al 2013). The crucial challenge is to identify the ways in which these features create feedback cycles in the network that can sustain transmission over time. The interaction structure needs to literally re-circulate the diffusion bit of interest over time, and the aggregation of temporal network cycles provides the foundation for this recirculation. This approach extends tools developed for the temporal projections of dynamic networks (Moody 2009, Mucha et al 2010), contact process models (Sander, Ferreira, and Pastor-Satorras 2013), generalizations of complex transmission process (Centola and Macy 2007) and formal epidemiological approaches (Pastro-Satorras and Vespignani 2001).

The simplest approximations to these processes have been encapsulated in extensions of epidemic models on homogeneous networks (Zhao et al 2012; Cator, Bovenkamp and Van Mieghem 2013) or continuous time contact process models. But these approximations do not handle dynamic networks with high population turnover, complex network structures, or transmission processes that require multiple reinforcements to propagate. The best alternative is to use agent based modeling (ABM) approaches that allow us to build realistic complexity into our models.

For this fellowship, I propose developing an ABM approach that leverages earlier insights about cycles and diffusion in dynamic networks to situations where diffusion requires reinforcement. The key graph theoretic questions turn on how cycles in the contact network and interaction timing overlap with the necessary refresh rate of whatever is diffusing through the network to keep the belief endemic. The result will be the ability to characterize networks by their differential capacity to sustain belief across a wide array of transmission regimes: to identify the network’s cultural carrying capacity.

I see this as a lynchpin problem, admitting to many substantive extensions: once these mechanisms are identified, can the same fundamental network tools be used to understand wide swings in beliefs (“fads” or “bubbles”) or the persistence of a belief in the face of a competing diffusion processes (such as when holding one belief precludes holding another). Ultimately this will allow one to compare networks across multiple domains on a key link between system structure and performance.

References for Abstract

Cator, E., R van de Bovenkamp and P. Van Mieghem. 2013. “Susceptible-infected-susceptible epidemics on networks with general infection and cure times.” Physical Review E. 87, 062816.

Centola, D. and Macy, M. 2007. “Complex contagions and the weakness of long ties.” American Journal of Sociology, 113:702–734.

Kontoleon, Nectarios, Lucia Falzon, and Philippa Pattison. 2013. “Algebraic structures for dynamic networks” Journal of Mathematical Psychology 57:310-319.

Moody, James. 2009. Static Representations of Dynamic Networks. Manuscript. DuPRI working paper 2009-009. http://papers.ccpr.ucla.edu/download.php?paper=PWP-DUKE-2009-009 .

Moody, James.2002. “The Importance of Relationship Timing for Diffusion.” Social Forces 81:25-56.

Moody, James and Douglas R. White. 2003. “Structural Cohesion and Embeddedness: A hierarchical concep-tion of Social Groups.” American Sociological Review 68:103-127.

Mucha, P. J., Richardson, T., Macon, K., Porter, M. A., and Onnela, J.-P. 2010. Community struc-ture in time-dependent, multiscale, and multiplex networks. Science, 328(5980):876–8.

Pastor-Satorras, Romualdo and A. Vespignani. 2001. “Epidemic dynamics and endemic states in complex net-works” Physical Review E. 63, 066117.

Sander, Renan S., Silvio C. Ferreira and Romualdo Pastor-Satorras. 2013. “Phase transitions with infinitely many absorbing states in complex networks” PHYSICAL REVIEW E 87, 022820.

Zhao, Laijun, Jiajia Wang, Yucheng Chen, Qin Wang, Jingjing Chen and Hongxin Cui. 2012. “SIHR rumor spread-ing model in social networks” Physica A 391:2444-2453.