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Real-world networks contain many cliques since they are usually built from them. The analysis that goes behind the cliques is fundamental because it discovers the real structure of the network. This article proposed new high-order closed trail clustering and closure coefficients for evaluation of the network structure. These coefficients are able to describe the inner structure of the network concerning its randomized or organized behavior. Moreover, the coefficients can cluster networks with similar structures together. The experiments show that the coefficients are useful in both the local and global context.