  The network of interactions among fluid elements and coherent structures
gives rise to the incredibly rich dynamics of vortical flows. These
interactions can be described with the use of mathematical tools from the
emerging field of network science, which leverages graph theory, dynamical
systems theory, data science, and control theory. The blending of network
science and fluid mechanics facilitates the extraction of the key interactions
and communities in terms of vortical elements, modal structures, and particle
trajectories. Phase-space techniques and time-delay embedding enable
network-based analysis in terms of visibility, recurrence, and cluster
transitions leveraging available time-series measurements. Equipped with the
knowledge of interactions and communities, the network-theoretic approach
enables the analysis, modeling, and control of fluid flows, with a particular
emphasis on interactive dynamics. In this article, we provide a brief
introduction to network science and an overview of the progress on
network-based strategies to study the complex dynamics of fluid flows. Case
studies are surveyed to highlight the utility of network-based techniques to
tackle a range of problems from fluid mechanics. Towards the end of the paper,
we offer an outlook on network-inspired approaches.
