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

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.

References in corpus (7)

• Path lengths, correlations, and centrality in temporal networks
• Hydrodynamic provinces and oceanic connectivity from a transport network help designing marine reserves
• Optimal Paths in Disordered Complex Networks
• Temporal networks: slowing down diffusion by long lasting interactions
• Global disease spread: statistics and estimation of arrival times
• Flow networks: A characterization of geophysical fluid transport
• Arrival Time Statistics in Global Disease Spread

Cited by in corpus (17)

• Modern temporal network theory: A colloquium
• Correlation networks from flows. The case of forced and time-dependent advection-diffusion dynamics
• Dominant transport pathways in an atmospheric blocking event
• Lagrangian betweenness as a measure of bottlenecks in dynamical systems with oceanographic examples
• Extending Transition Path Theory: Periodically-Driven and Finite-Time Dynamics
• Explicit and implicit network connectivity: Analytical formulation and application to transport processes
• Spatio-temporal organization of dynamics in a two-dimensional periodically driven vortex flow: a Lagrangian flow network perspective
• Clustering coefficient and periodic orbits in flow networks
• Impact of climate change on surface stirring and transport in the Mediterranean Sea
• Markov-chain-inspired search for MH370
• Estimating the travel time and the most likely path from Lagrangian drifters
• Lagrangian Flow Network approach to an open flow model
• From large deviations to semidistances of transport and mixing: coherence analysis for finite Lagrangian data
• Crossroads of the mesoscale circulation
• Characteristic signatures of Northern Hemisphere blocking events in a Lagrangian flow network representation of the atmospheric circulation
• Network and geometric characterization of three-dimensional fluid transport between two layers
• A Markov model for inferring flows in directed contact networks