How even tiny influence can have a big impact!

Abstract

An influence network is a graph where each node changes its state according to a function of the states of its neighbors. We present bounds for the stabilization time of such networks. We derive a general bound for the classic "Democrats and Republicans" problem and study different model modifications and their influence on the way of stabilizing and their stabilization time. Our main contribution is an exponential lower and upper bound on weighted influence networks. We also investigate influence networks with asymmetric weights and show an influence network with an exponential cycle length in the stable situation. © 2014 Springer International Publishing.