  The study of connectivity patterns in networks has brought novel insights
across diverse fields ranging from neurosciences to epidemic spreading or
climate. In this context, betweenness centrality has demonstrated to be a very
effective measure to identify nodes that act as focus of congestion, or
bottlenecks, in the network. However, there is not a way to define betweenness
outside the network framework. By analytically linking dynamical systems and
network theory, we provide a trajectory-based formulation of betweenness,
called Lagrangian betweenness, as a function of Lyapunov exponents. This
extends the concept of betweenness beyond the context of network theory
relating hyperbolic points and heteroclinic connections in any dynamical system
to the structural bottlenecks of the network associated with it. Using modeled
and observational velocity fields, we show that such bottlenecks are present
and surprisingly persistent in the oceanic circulation across different
spatio-temporal scales and we illustrate the role of these areas in driving
fluid transport over vast oceanic regions. Analyzing plankton abundance data
from the Kuroshio region of the Pacific Ocean, we find significant spatial
correlations between measures of diversity and betweenness, suggesting promise
for ecological applications.
