| Random walk on discrete lattice models is important to understand various types of transport processes. Using random walk model for transport extreme events, defined as exceedences of the flux above a prescribed threshold, have been studied recently in the context of complex networks. This is motivated by the extreme events such as the traffic jams, floods, power black-outs that take place on networks. In this work, we study the 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 the probability for the occurrence of extreme events on any node in the network depends on its 'strength', a measure of the ability of a node to attract walkers. The 'strength' is a function of the degree of the node and that of its neighbors. We obtain analytical and simulation results for the probability of extreme events on the nodes of a network using the generalized random walk model. The result reveals that the nodes with larger value of strength, on an average, display lower probability for the occurrence of extreme events compared to the nodes with lower value of strength. In particular, we obtain the distribution of event sizes on the network. This shows that extremely large fluctuations in event-sizes are possible on small degree nodes when the walkers are biased toward the hubs. |
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