Temporal networks: slowing down diffusion by long lasting interactions

Interactions among units in complex systems occur in a specific
sequential order thus affecting the flow of information, the propagation
of diseases, and general dynamical processes. We investigate the
Laplacian spectrum of temporal networks and compare it with that of the
corresponding aggregate network. First, we show that the spectrum of the
ensemble average of a temporal network has identical eigenmodes but
smaller eigenvalues than the aggregate networks. In large networks
without edge condensation, the expected temporal dynamics is a
time-rescaled version of the aggregate dynamics. Even for single
sequential realizations, diffusive dynamics is slower in temporal
networks. These discrepancies are due to non-commutability of
interactions. We illustrate our analytical findings using a simple
temporal motif, larger network models and real temporal networks.