DOI: 10.36347/sjpms

Pages: 74-80

In hyper-networks, arriving time and the convert distance are used to measure the structure of hyper-graphs. For two vertices u and v, the arriving time Huv is defined as the expected time for it takes a random walk to travel from u to v. The convert distance is a symmetrized version denoted as Cuv = Huv + Hvu . In this article, we consider the characters of arriving times and convert distances when the number n of vertices in the hyper-networks tends to . We discuss random geometric hyper-graphs, such as  -hyper-graphs, k-NN hyper-graphs and Gaussian similarity hypergraphs, and the hyper-graphs with a given expected degree distribution or other special hyper-graphs structures. Several results on convergence are determined, and these illustrate the promising application prospects for hyper-networks algorithm. Keywords: arriving time, convert time, hyper-networks, random hyper-graph, spectral gap