title: Navigation by anomalous random walks on complex networks.
abstract: Anomalous random walks having long-range jumps are a critical branch of dynamical processes on networks, which can model a number of search and transport processes. However, traditional measurements based on mean first passage time are not useful as they fail to characterize the cost associated with each jump. Here we introduce a new concept of mean first traverse distance (MFTD) to characterize anomalous random walks that represents the expected traverse distance taken by walkers searching from source node to target node, and we provide a procedure for calculating the MFTD between two nodes. We use Lévy walks on networks as an example, and demonstrate that the proposed approach can unravel the interplay between diffusion dynamics of Lévy walks and the underlying network structure. Moreover, applying our framework to the famous PageRank search, we show how to inform the optimality of the PageRank search. The framework for analyzing anomalous random walks on complex networks offers a useful new paradigm to understand the dynamics of anomalous diffusion processes, and provides a unified scheme to characterize search and transport processes on networks.
authors.affiliation: HKUST-DT System and Media Laboratory, Hong Kong University of Science and Technology, HongKong.
authors.forename: Tongfeng
authors.initials: T
authors.lastname: Weng
authors.affiliation: Centre for Computational Systems Biology, Fudan University, China.
authors.forename: Jie
authors.initials: J
authors.lastname: Zhang
authors.affiliation: HKUST-DT System and Media Laboratory, Hong Kong University of Science and Technology, HongKong.
authors.forename: Moein
authors.initials: M
authors.lastname: Khajehnejad
authors.affiliation: The University of Western Australia, Crawley, WA 6009, Australia.|Mineral Resources, CSIRO, Kensington, WA, Australia.
authors.forename: Michael
authors.initials: M
authors.lastname: Small
authors.affiliation: HKUST-DT System and Media Laboratory, Hong Kong University of Science and Technology, HongKong.
authors.forename: Rui
authors.initials: R
authors.lastname: Zheng
authors.affiliation: HKUST-DT System and Media Laboratory, Hong Kong University of Science and Technology, HongKong.
authors.forename: Pan
authors.initials: P
authors.lastname: Hui