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The network throughput in ad hoc wireless networks under a hierarchical routing (e.g. cluster-based) scheme is investigated. Some works have studied the routing overhead of hierarchical base routing. However, there is little formal analysis that considers its influence on the network performance metric, e.g. throughput, incurred by these procedures. Provided is a theoretical computation on the throughput of the ad hoc wireless networks under a cluster-based structure. Discussed is the issue that the throughput of such ad hoc networks is relatively smaller by a factor of O(N2/N1), N2 is the number of cluster-head nodes and N1 is the number of all the nodes in a network. Hence, there is a trade-off between the gain from routing overhead and loss from network throughput in the design of hierarchical routing for ad hoc networks which need to be optimised. The result has many implications for the hierarchical structure wireless networks.