# Cover time for random walks on arbitrary complex networks

## TL;DR

This paper introduces an analytical method to estimate the mean cover time of random walks on complex networks, linking first passage times to cover times, applicable to various network types including real-world networks.

## Contribution

The authors develop a new analytical approach to compute cover times on arbitrary networks using first passage time statistics, improving estimation efficiency.

## Key findings

- Method applies to Erdős-Rényi and Barabási-Albert networks.
- Establishes a link between first passage and cover time statistics.
- Provides a computationally efficient estimation technique.

## Abstract

We present an analytical method for computing the mean cover time of a random walk process on arbitrary, complex networks. The cover time is defined as the time a random walker requires to visit every node in the network at least once. This quantity is particularly important for random search processes and target localization in network topologies. Based on the global mean first passage time of target nodes we derive an estimate for the cumulative distribution function of the cover time based on first passage time statistics. We show that our result can be applied to various model networks, including Erd\H{o}s-R\'enyi and Barab\'asi-Albert networks, as well as various real-world networks. Our results reveal an intimate link between first passage and cover time statistics in networks in which structurally induced temporal correlations decay quickly and offer a computationally efficient way for estimating cover times in network related applications.