Most probable paths in temporal weighted networks: An application to ocean transport

TL;DR

This paper introduces tools to identify the most probable paths in temporal weighted networks and demonstrates their effectiveness in characterizing ocean transport in the Mediterranean Sea, highlighting the dominance of few high-probability paths.

Contribution

It develops a formalism for computing high-probability paths and redefines betweenness centrality based on these paths, applied to ocean surface flow networks.

Findings

A small subset of high-probability paths suffices to characterize connectivity.

Most probable paths dominate the transport dynamics within realistic time scales.

The formalism provides new insights into network centrality measures.

Abstract

We consider paths in weighted and directed temporal networks, introducing tools to compute sets of paths of high probability. We quantify the relative importance of the most probable path between two nodes with respect to the whole set of paths, and to a subset of highly probable paths which incorporate most of the connection probability. These concepts are used to provide alternative definitions of betweenness centrality. We apply our formalism to a transport network describing surface flow in the Mediterranean sea. Despite the full transport dynamics is described by a very large number of paths we find that, for realistic time scales, only a very small subset of high probability paths (or even a single most probable one) is enough to characterize global connectivity properties of the network.