  One of the ubiquitous features of real-life turbulent flows is the existence
and persistence of coherent vortices. Here we show that such coherent vortices
can be extracted as clusters of Lagrangian trajectories. We carry out the
clustering on a weighted graph, with the weights measuring pairwise distances
of fluid trajectories in the extended phase space of positions and time. We
then extract coherent vortices from the graph using tools from spectral graph
theory. Our method locates all coherent vortices in the flow simultaneously,
thereby showing high potential for automated vortex tracking. We illustrate the
performance of this technique by identifying coherent Lagrangian vortices in
several two- and three-dimensional flows.
