摘要：

For bringing the ideas of Hodge theory to combinatorics and others, June Huh won the Fields Medals 2022. Later, Lim introduced the Hodge theory on a graph G, called Hodge Laplacians of G, a higher-order generalization of the graph Laplacian [L.-H. Lim, Hodge Laplacians on graphs, SIAM Rev. 62 (2020) 685–715]. In this report, we will investigate the spectral properties of Hodge 1-Laplacian.