The Power of Temporal Networks

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Abstract: Many networked systems of scientific interest–from food webs, to infrastructure, to human social systems–are characterized by time-varying (temporal) interaction networks. Link temporality complicates many traditional forms of network analysis, requiring redefinition of basic concepts like distance, centrality, and motifs. Moreover, the fact that paths between nodes are not "always on" in temporal networks frustrates processes like navigation, routing, and diffusion. For these reasons, time-varying network structure can be regarded as something of a nuisance. In this talk, I will try to turn this view on its head. Specifically, I will present two examples from dynamical systems on networks in which link temporality confers unambiguous advantages.  First, I will show how temporal networks exhibit superior controllability properties relative to their static counterparts, with across-the-board reductions in all common costs of control . Second, I will use models from evolutionary game theory to show how time-varying social networks can promote the emergence of cooperation (altruism) among naturally self-interested individuals. Time permitting, I will also preview exciting ongoing work, showing how one can exploit temporal networks to stably synchronize coupled oscillators even when all configurations of the network are unstable. These and other examples point to an inherent power and flexibility in temporal networks over static topologies. Indeed, from the vantage of network dynamics(rather than structure), it seems that temporality can be a blessing instead of a curse.