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Extreme events have low occurrence probabilities and display pronounceddeviation from their average behaviour, such as earthquakes or power blackouts.Such extreme events occurring on the nodes of a complex network have beenextensively studied earlier through the modelling framework of unbiased randomwalks. They reveal that the occurrence probability for extreme events on nodesof 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 thoseoccurring on nodes. Hence, in this work, we propose a more general formalism tostudy the properties of extreme events arising from biased random walkers onthe edges of a network. This formalism is applied to biases based on a varietynetwork centrality measures including PageRank. It is shown that with biasedrandom walkers as the dynamics on the network, extreme event probabilitiesdepend on the local properties of the edges. The probabilities are highlyvariable for some edges of the network, while they are approximately a constantfor some other edges on the same network. This feature is robust with respectto different biases applied to the random walk algorithm. Further, usingresults from this formalism, it is shown that a network is far more robust toextreme events occurring on edges when compared to those occurring on thenodes.

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