Title: Random walks on activity-driven networks with attractiveness,
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.