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To mitigate the overhead of routing protocols in any large-scale network, the hierarchical protocol was proposed in the early 1980s. However, the message relay would entail huge throughput reduction in such a hierarchical network. Thanks to the recently developed network coding techniques, a high-throughput low-complexity hierarchical protocol can be facilitated due to the multiple-source relay-based data transmissions built on the network coding schemes, particularly for the data communications between adjacent network levels. In this paper, we apply random geometry theory to evaluate the network performance of the proposed hierarchical routing method in the statistical average sense. Two essential measures, namely, routing complexity and average network throughput, are formulated and derived thereby. The numerical results demonstrate that significant improvements in terms of these three network performance measures can be achieved by the proposed hierarchical routing protocol using network coding according to our new statistical analysis.