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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.
We study SIS epidemic spreading processes unfolding on a recent generalisation of the activity-driven modelling framework. In this model of time-varying networks each node is described by two variables: activity and attractiveness. The first, describ
We consider an epidemic process on adaptive activity-driven temporal networks, with adaptive behaviour modelled as a change in activity and attractiveness due to infection. By using a mean-field approach, we derive an analytical estimate of the epide
Random walks constitute a fundamental mechanism for many dynamics taking place on complex networks. Besides, as a more realistic description of our society, multiplex networks have been receiving a growing interest, as well as the dynamical processes
We study the effect of heterogeneous temporal activations on epidemic spreading in temporal networks. We focus on the susceptible-infected-susceptible (SIS) model on activity-driven networks with burstiness. By using an activity-based mean-field appr
In recent years, the theory and application of complex networks have been quickly developing in a markable way due to the increasing amount of data from real systems and to the fruitful application of powerful methods used in statistical physics. Man