In order to satisfy the rapidly increasing demand for data volume, large data center networks (DCNs) have been proposed. In 2019, Zhang et al. proposed a new highly scalable DCN architecture named HSDC (Highly Scalable Data Center Network), which can achieve greater incremental scalability. In this paper, we give the definition of the logical graph of HSDC, named \(H_n\), which can be treated as a compound graph of hypercube and complete graph of the same dimension. First, we prove that the connectivity and tightly super connectivity of \(H_n\) are both n. Then, we give an O(n) shortest unicast algorithm to find a shortest path between any two distinct nodes in \(H_n\), and prove the correctness of this algorithm. In fact, we also prove that the length of the shortest path constructed by this algorithm is no more than \(2d+1\) if \(d<n\) and at most 2d if \(d=n\), where d is the Hamming distance between the start and end nodes, and the diameter of \(H_n\) is 2n.

为了满足对数据量的快速增长的需求，已经提出了大型数据中心网络（DCN）。在2019年，Zhang等。提出了一种新的高度可扩展的DCN架构，称为HSDC（高度可扩展的数据中心网络），它可以实现更大的增量可扩展性。在本文中，我们给出了HSDC逻辑图的定义，称为\（H_n \），可以将其视为超立方体的复合图和相同维的完整图。首先，我们证明\（H_n \）的连通性和严格超连通性均为n。然后，我们给出O（n）最短单播算法，以找到\（H_n \）中任意两个不同节点之间的最短路径，并证明该算法的正确性。实际上，我们还证明了该算法构造的最短路径的长度，如果\（d <n \）不超过\（2d + 1 \），如果\（d = n \）不超过2 d，其中d是起点和终点之间的汉明距离，\（H_n \）的直径为2 n。