Explicit and implicit network connectivity: Analytical formulation and application to transport processes

TL;DR

This paper develops an analytical framework to compute connection probabilities in temporal, directed, weighted networks, linking structural connectivity to transport dynamics, and applies it to ocean transport in the Mediterranean Sea.

Contribution

It derives exact expressions for connectivity probabilities in complex networks, integrating explicit and implicit connectivity, and demonstrates their application to real-world ocean transport analysis.

Findings

Identifies fluid barriers and corridors affecting ocean transport.

Reveals counter-intuitive connectivity patterns in the Mediterranean Sea.

Provides a framework for analyzing transport processes in complex networks.

Abstract

Connectivity is a fundamental structural feature of a network that determines the outcome of any dynamics that happens on top of it. However, an analytical approach to obtain connection probabilities between nodes associated to paths of different lengths is still missing. Here, we derive exact expressions for random-walk connectivity probabilities across any range of numbers of steps in a generic temporal, directed and weighted network. This allows characterizing explicit connectivity realized by causal paths as well as implicit connectivity related to motifs of three nodes and two links called here pitchforks. We directly link such probabilities to the processes of tagging and sampling any quantity exchanged across the network, hence providing a natural framework to assess transport dynamics. Finally, we apply our theoretical framework to study ocean transport features in the Mediterranean Sea. We find that relevant transport structures, such as fluid barriers and corridors, can generate contrasting and counter-intuitive connectivity patterns bringing novel insights into how ocean currents drive seascape connectivity.