  A hypergraph as a generalization of graphs records higher-order interactions
among nodes, yields a more flexible network model, and allows non-linear
features for a group of nodes. In this article, we propose a hypergraph echo
state network (HypergraphESN) as a generalization of graph echo state network
(GraphESN) designed for efficient processing of hypergraph-structured data,
derive convergence conditions for the algorithm, and discuss its versatility in
comparison to GraphESN. The numerical experiments on the binary classification
tasks demonstrate that HypergraphESN exhibits comparable or superior accuracy
performance to GraphESN for hypergraph-structured data, and accuracy increases
if more higher-order interactions in a network are identified.
