Weighted multi-connected loop networks (Q1910548)

Suppose \(N\), \(a\), \(a_2,\dots, a_k\) are relatively prime integers. A weighted multi-connected loop network \(W\) is a directed graph with vertex set \([0, 1,\dots, N- 1]\), directed edges \(i\to i+ a_j\pmod N\) and edge weights \(w_j\), \(w_j> 0\) and \(j= 1,2,\dots, k\). The author investigates the diameter and average diameter of \(W\). In particular, general bounds are established for the diameter and average diameter.