Asymptotic theory for the dynamic of networks with heterogenous social capital allocation

Abstract

The structure and dynamic of social network are largely determined by the heterogeneous interaction activity and social capital allocation of individuals. These features interplay in a non-trivial way in the formation of network and challenge a rigorous dynamical system theory of network evolution. Here we study seven real networks describing temporal human interactions in three different settings: scientific collaborations, Twitter mentions, and mobile phone calls. We find that the node's activity and social capital allocation can be described by two general functional forms that can be used to define a simple stochastic model for social network dynamic. This model allows the explicit asymptotic solution of the Master Equation describing the system dynamic, and provides the scaling laws characterizing the time evolution of the social network degree distribution and individual node's ego network. The analytical predictions reproduce with accuracy the empirical observations validating the theoretical approach. Our results provide a rigorous dynamical system framework that can be extended to include other features of networks' formation and to generate data driven predictions for the asymptotic behavior of large-scale social networks.

(31 pages (main text: 11; SI: 20), 15 figures, 3 tables)

References in corpus (21)

• Modularity and community structure in networks
• Power-law distributions in empirical data
• Structure and tie strengths in mobile communication networks
• Dynamics of person-to-person interactions from distributed RFID sensor networks
• What's in a crowd? Analysis of face-to-face behavioral networks
• Activity driven modeling of time varying networks
• Small But Slow World: How Network Topology and Burstiness Slow Down Spreading
• Validation of Dunbar's number in Twitter conversations
• Homophily, Cultural Drift and the Co-Evolution of Cultural Groups
• Diffusion of scientific credits and the ranking of scientists
• Information dynamics shape the networks of Internet-mediated prostitution
• Random walks and search in time-varying networks
• Dynamical and bursty interactions in social networks
• Modeling human dynamics of face-to-face interaction networks
• Persistence and periodicity in a dynamic proximity network
• Complex contagion process in spreading of online innovation
• Burstiness and aging in social temporal networks
• Contagion dynamics in time-varying metapopulation networks
• Generalization of Blonder-Tinkham-Klapwijk theory to particle-hole mixing boundary conditions: π-shift and conductance dips
• From calls to communities: a model for time varying social networks
• Attractiveness and activity in Internet communities

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