Diffusion on networked systems is a question of time or structure
Nature Communications, (Jun 9, 2015)DOI: 10.1038/ncomms8366
Abstract
We focus on general continuous-time random walks on networks and find that
the mixing time, i.e. the relaxation time for the random process to reach
stationarity, is determined by a combination of three factors: the spectral
gap, associated to bottlenecks in the underlying topology, burstiness, related
to the second moment of the waiting time distribution, and the characteristic
time of its exponential tail, which is an indicator of the tail `fatness'. We
show theoretically that a strong modular structure dampens the importance of
burstiness, and empirically that either of the three factors may be dominant in
real-life data. These results provide a theoretical framework for the modeling
of diffusion on temporal networks representing human interactions, often
characterized by non-Poissonian contact patterns.