Activity driven modeling of dynamic networks

Abstract

Network modeling plays a critical role in identifying statistical regularities and structural principles common to many systems. The large majority of recent modeling approaches are connectivity driven, in the sense that the structural pattern of the network is at the basis of the mechanisms ruling the network formation. Connectivity driven models necessarily provide a time-aggregated representation that may fail to describe the instantaneous and fluctuating dynamics of many networks. We address this challenge by defining the activity potential, a time invariant function characterizing the agents' interactions in real-world networks and constructing an activity driven model capable of encoding the instantaneous time description of the network dynamics. The model provides an explanation of structural features such as the presence of hubs, which simply originate from the heterogeneous activity of agents. Additionally, we find that diffusive processes in highly dynamical networks can be described analytically in terms of the activity potential, allowing a quantitative discussion of the biases induced by the time-aggregated network representation in the analysis of dynamical processes in evolving networks.