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.

这篇文章介绍了一种超图回声状态网络（HypergraphESN）作为图回声状态网络（GraphESN）的推广，旨在高效处理超图结构数据，并导出了算法的收敛条件，讨论了与 GraphESN 相比的多样性。对于超图结构数据，对二元分类任务的数值实验表明，HypergraphESN 与 GraphESN 相比具有相当或更好的准确性性能，并且准确性会随着发现网络中更多的高阶交互作用而增加。

超图回响状态网络

Hypergraph Echo State Network

We propose high-order hypergraph walks as a framework to generalize
graph-based network science techniques to hypergraphs. Edge incidence in
hypergraphs is quantitative, yielding hypergraph walks with both length and
width. Graph methods which then generalize to hypergraphs include connected
component analyses, graph distance-based metrics such as closeness centrality,
and motif-based measures such as clustering coefficients. We apply high-order
analogs of these methods to real world hypernetworks, and show they reveal
nuanced and interpretable structure that cannot be detected by graph-based
methods. Lastly, we apply three generative models to the data and find that
basic hypergraph properties, such as density and degree distributions, do not
necessarily control these new structural measurements. Our work demonstrates
how analyses of hypergraph-structured data are richer when utilizing tools
tailored to capture hypergraph-native phenomena, and suggests one possible
avenue towards that end.

本文提出了高阶超图行走作为一个新的框架来推广基于图的网络科学技术到超图中，并通过应用高阶模型分析真实世界的超网络数据和三个生成模型发现了超图结构的微妙和可解释性，表明当利用针对捕捉超图本地现象的工具时，超图结构化数据的分析更加丰富。