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In this paper, E-3DMesh network which is a novel switching fabric of the terabit router is studied, and it is one of very popular and important topological structure in next generation terabit router. Based on partitioning strategies, a new probabilistic analysis approach is given, which enables us to derive the node failure probability of E-3DMesh networks when the connectivity probability of E-3DMesh network is attributed. By rigorous mathematical ratiocinate to prove that when the network node failure probability is bounded by 3.78%, millions of nodes in E-3DMesh networks remain connected with probability larger than 99%. The results show that E-3DMesh network is potentially an attractive interconnection network topology; it is noticeable that the scheme is a powerful technique for calculating the probabilistic connectivity in E-3DMesh networks, and is also applicable to the study of other hierarchical network structures and of other network communication problems.