Extra connectivity of the data center network—RRect

With the continuous expansion of network scale, fault tolerance and security in network operation have become increasingly important. The high vertex connectivity of the interconnection network indicates excellent fault tolerance. In order to address the drawbacks of traditional connectivity, the g-extra connectivity has been proposed to better reflect the fault tolerance of the network. RRect is a newly proposed server-centered data center network with good interconnection structure, and it has excellent flexibility and energy efficiency. In this paper, we focus on the logical structure of RRect, denoted by \(RR_{n,m,k}\) $R{R}_{n,m,k}$ . Firstly, we investigate the extra connectivity of \(RR_{n,m,k}\) $R{R}_{n,m,k}$ , and, in detail, we prove that for \(n \ge 4\) $n\ge 4$ , \(m \ge 1\) $m\ge 1$ , and \(k \ge 4\) $k\ge 4$ , the \(\{1, 2, 3\}\) $\{1,2,3\}$ -extra connectivity of \(RR_{n,m,k}\) $R{R}_{n,m,k}$ is \(2km(n-1) + mn - 2\) $2km(n-1)+mn-2$ , \(3km(n-1) + mn - 3\) $3km(n-1)+mn-3$ , and \(4km(n-1) - 4m\) $4km(n-1)-4m$ , respectively, which are about 2, 3, and 4 times of its traditional connectivity. Secondly, we conduct numerical simulation experiments on the extra connectivity of \(RR_{n,m,k}\) $R{R}_{n,m,k}$ and evaluate the experimental performance. The result can provide a more comprehensive measurement of its reliability.