Extreme events in stochastic transport on networks

TL;DR

This paper investigates extreme events in stochastic transport on networks, revealing that edge extreme events differ from nodal ones and depend on network-wide properties rather than node degrees.

Contribution

It introduces a novel analysis of edge extreme events, showing their independence from node degrees and their dependence on overall network structure.

Findings

Edge extreme event probability is independent of node degrees.

Extreme events on edges depend only on total edges and number of walkers.

Correlations can exist between node and edge extreme events.

Abstract

Extreme events are emergent phenomena in multi-particle transport processes on complex networks. In practice, such events could range from power blackouts to call drops in cellular networks to traffic congestion on roads. All the earlier studies of extreme events on complex networks have focused only on the nodal events. If random walks are used to model transport process on a network, it is known that degree of the nodes determines the extreme event properties. In contrast, in this work, it is shown that extreme events on the edges display a distinct set of properties from that of the nodes. It is analytically shown that the probability for the occurrence of extreme events on an edge is independent of the degree of the nodes linked by the edge and is dependent only on the total number of edges on the network and the number of walkers on it. Further, it is also demonstrated that non-trivial correlations can exist between the extreme events on the nodes and the edges. These results are in agreement with the numerical simulations on synthetic and real-life networks.