Abstract

Transport on weighted graphs is a general framework to study a variety of physical and social phenomena, serving to characterize the transport efficiency or propagation of quantities or packages on different weighted complex networks. Packages that start at a particular node propagate through the weighted network and produce a distribution of arrival times or travel costs at other nodes, depending on the network topology characterized by the probability weights of the directed links in the network and the possibly nonuniform cost function of each directed link. We present a mathematical formulation in terms of the moments of the distribution function of travel-times (or cost), which completely characterizes the distribution function theoretically. In-terestingly, this approach is equivalent to finding the propagator (Green's function) in quantum mechanics, as it provides full information about how packages propagate along the network. Our formulation does not depend on the usual assumptions of symmetric connectivity, symmetric weights, or spectral analysis. This approach allows obtaining exact expressions of the mean travel-time (or cost) and its fluctuations for any connected binary or weighted graphs. We contrast our theoretical results with Monte Carlo simulations on Erdos-Renyi, Watts-Strogatz, and Barabasi-Albert topologies considering binary and weighted cases, which confirm our analytical predictions. Our approach also allows retrieving the information of the probability weights among nodes theoretically once the mean travel time is known without considering any assumptions of the connectivity of the network. Hence, such analysis could be useful for Epidemiology or Public Health purposes to ascertain information that is typically difficult to obtain.(c) 2022 Elsevier B.V. All rights reserved.