  We demonstrate the effective use of randomized methods for linear algebra to
perform network-based analysis of complex vortical flows. Network theoretic
approaches can reveal the connectivity structures among a set of vortical
elements and analyze their collective dynamics. These approaches have recently
been generalized to analyze high-dimensional turbulent flows, for which network
computations can become prohibitively expensive. In this work, we propose
efficient methods to approximate network quantities, such as the leading
eigendecomposition of the adjacency matrix, using randomized methods.
Specifically, we use the Nystr\"om method to approximate the leading
eigenvalues and eigenvectors, achieving significant computational savings and
reduced memory requirements. The effectiveness of the proposed technique is
demonstrated on two high-dimensional flow fields: two-dimensional flow past an
airfoil and two-dimensional turbulence. We find that quasi-uniform column
sampling outperforms uniform column sampling, while both feature the same
computational complexity.
