7 research outputs found
Modern temporal network theory: A colloquium
The power of any kind of network approach lies in the ability to simplify a
complex system so that one can better understand its function as a whole.
Sometimes it is beneficial, however, to include more information than in a
simple graph of only nodes and links. Adding information about times of
interactions can make predictions and mechanistic understanding more accurate.
The drawback, however, is that there are not so many methods available, partly
because temporal networks is a relatively young field, partly because it more
difficult to develop such methods compared to for static networks. In this
colloquium, we review the methods to analyze and model temporal networks and
processes taking place on them, focusing mainly on the last three years. This
includes the spreading of infectious disease, opinions, rumors, in social
networks; information packets in computer networks; various types of signaling
in biology, and more. We also discuss future directions.Comment: Final accepted versio
Burstiness and fractional diffusion on complex networks
Many dynamical processes on real world networks display complex temporal
patterns as, for instance, a fat-tailed distribution of inter-events times,
leading to heterogeneous waiting times between events. In this work, we focus
on distributions whose average inter-event time diverges, and study its impact
on the dynamics of random walkers on networks. The process can naturally be
described, in the long time limit, in terms of Riemann-Liouville fractional
derivatives. We show that all the dynamical modes possess, in the asymptotic
regime, the same power law relaxation, which implies that the dynamics does not
exhibit time-scale separation between modes, and that no mode can be neglected
versus another one, even for long times. Our results are then confirmed by
numerical simulations.Comment: 7 pages, 4 figure