Summary: Traditional data center networks (DCNs) are faced with many challenges with the development of cloud computing. This fact makes design of new DCNs represented by DCell networks become a hot research topic. For any integers \(k \geq 0\) and \(n \geq 2\), the \(k\)-dimensional DCell with \(n\)-port switches and \(t_{k, n}\) nodes, \(D_{k, n}\), has been proposed for an important DCNs as a server-centric DCN structure. In this paper, we prove that under the condition that each fault-free node of the \(D_{k, n}\) has at least \(h\) fault-free neighbor(s) its restricted \(h\)-connectivity is \((h + 1)(k - 1) + n\) (resp. \((n + k - h - 1) t_{h - n + 1, n}\)) with \(0 \leq h \leq n - 1\) (resp. \(n \leq h \leq n + k - 2\)), which is almost as \((h + 1)\) (resp. \(t_{h - n + 1, n}\)) times as traditional connectivity of \(D_{k, n}\). When the DCell network is used to model the topological structure of a large-scale DCN, this result can provide a more accurate measure for the fault tolerance of the network.