Memory and burstiness in dynamic networks
Physical Review E, (Jul 24, 2015)DOI: 10.1103/PhysRevE.92.012817
Abstract
We introduce a class of complex network models which evolve through the
addition of edges between nodes selected randomly according to their intrinsic
fitness, and the deletion of edges according to their age. We add to this a
memory effect where the attractiveness of a node is increased by the number of
edges it is currently attached to, and observe that this creates burst-like
activity in the attachment events of each individual node which is
characterised by a power-law distribution of inter-event times. The fitness of
each node depends on the probability distribution from which it is drawn; we
find exact solutions for the expectation of the degree distribution for a
variety of possible fitness distributions, and for both cases where the memory
effect either is, or is not present. This work can potentially lead to methods
to uncover hidden fitness distributions from fast changing, temporal network
data such as online social communications and fMRI scans.