Extreme events taking place on networks are not uncommon. We show that it is possible to manipulate the extreme events occurrence probabilities and its distribution over the nodes on scale-free networks by tuning the nodal capacity. This can be used to reduce the number of extreme events occurrences on a network. However monotonic nodal capacity enhancements, beyond a point, do not lead to any substantial reduction in the number of extreme events. We point out the practical implication of this result for network design in the context of reducing extreme events occurrences.
Random walk on discrete lattice models is important to understand various types of transport processes. The extreme events, defined as exceedences of the flux of walkers above a prescribed threshold, have been studied recently in the context of complex networks. This was motivated by the occurrence of rare events such as traffic jams, floods, and power black-outs which take place on networks. In this work, we study extreme events in a generalized random walk model in which the walk is preferentially biased by the network topology. The walkers preferentially choose to hop toward the hubs or small degree nodes. In this setting, we show that extremely large fluctuations in event-sizes are possible on small degree nodes when the walkers are biased toward the hubs. In particular, we obtain the distribution of event-sizes on the network. Further, the probability for the occurrence of extreme events on any node in the network depends on its generalized strength, a measure of the ability of a node to attract walkers. The generalized strength is a function of the degree of the node and that of its nearest neighbors. We obtain analytical and simulation results for the probability of occurrence of extreme events on the nodes of a network using a generalized random walk model. The result reveals that the nodes with a larger value of generalized strength, on average, display lower probability for the occurrence of extreme events compared to the nodes with lower values of generalized strength.
We study the extreme events taking place on complex networks. The transport on networks is modelled using random walks and we compute the probability for the occurance and recurrence of extreme events on the network. We show that the nodes with smaller number of links are more prone to extreme events than the ones with larger number of links. We obtain analytical estimates and verify them with numerical simulations. They are shown to be robust even when random walkers follow shortest path on the network. The results suggest a revision of design principles and can be used as an input for designing the nodes of a network so as to smoothly handle an extreme event.
