Most probable paths in temporal weighted networks: An application to ocean transport.
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 that 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.
IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), E-07122 Palma de Mallorca, Spain.
Enrico
E
Ser-Giacomi
IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), E-07122 Palma de Mallorca, Spain.|Ambrosys GmbH, Albert-Einstein-Strasse 1-5, 14473 Potsdam, Germany.
Ruggero
R
Vasile
IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), E-07122 Palma de Mallorca, Spain.
Emilio
E
Hernández-García
IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), E-07122 Palma de Mallorca, Spain.
Cristóbal
C
López