Biased random walkers and extreme events on the edges of complex networks

TL;DR

This paper develops a formalism for analyzing extreme events on network edges caused by biased random walks, revealing that edge properties influence event probabilities and that networks are more robust to edge extreme events than node ones.

Contribution

It introduces a general framework for studying edge extreme events under biased random walks, extending previous node-focused models and demonstrating robustness differences.

Findings

Extreme event probabilities on edges depend on local edge properties.

Biases based on centrality measures affect edge extreme event probabilities.

Networks are more resilient to edge extreme events than node extreme events.

Abstract

Extreme events have low occurrence probabilities and display pronounced deviation from their average behaviour, such as earthquakes or power blackouts. Such extreme events occurring on the nodes of a complex network have been extensively studied earlier through the modelling framework of unbiased random walks. They reveal that the occurrence probability for extreme events on nodes of a network has a strong dependence on the nodal properties. Apart from these, a recent work has shown the independence of extreme events on edges from those occurring on nodes. Hence, in this work, we propose a more general formalism to study the properties of extreme events arising from biased random walkers on the edges of a network. This formalism is applied to biases based on a variety network centrality measures including PageRank. It is shown that with biased random walkers as the dynamics on the network, extreme event probabilities depend on the local properties of the edges. The probabilities are highly variable for some edges of the network, while they are approximately a constant for some other edges on the same network. This feature is robust with respect to different biases applied to the random walk algorithm. Further, using results from this formalism, it is shown that a network is far more robust to extreme events occurring on edges when compared to those occurring on the nodes.