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.
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