On the Complexity and Approximation of $\lambda_\infty\,,$ Spread Constant and Maximum Variance Embedding

Twenty years ago, Bobkov, Houdr\'e, and the last author introduced a Poincar\'e-type functional graph parameter, $\lambda_\infty(G)$, of a graph $G$, and related it to the {\em vertex expansion} of $G$ via a Cheeger-type inequality. This is analogous to the Cheeger-type inequality relating the spectral gap, $\lambda_2(G)$, of the graph ...More