Random walks on activity-driven networks with attractiveness

Laura Alessandretti, Kaiyuan Sun, Andrea Baronchelli, and Nicola Perra
Phys. Rev. E
95, 052318
May 25, 2017

Abstract

Virtually all  real-world networks are dynamical entities. In social networks, the  propensity of nodes to engage in social interactions (activity) and their  chances to be selected by active nodes (attractiveness) are heterogeneously  distributed. Here, we present a time-varying network model where each node  and the dynamical formation of ties are characterised by these two features.  We study how these properties affect random walk processes unfolding on the  network when the time scales describing the process and the network evolution  are comparable. We derive analytical solutions for the stationary state and  the mean first passage time of the process and we study cases informed by  empirical observations of social networks. Our work shows that previously disregarded  properties of real social systems such heterogeneous distributions of  activity and attractiveness as well as the correlations between them,  substantially affect the dynamical process unfolding on the network.

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