1. A method, implemented on one or more processors, of designing a network modeled by a Cayley Digraph, the method avoiding the generation of the whole network and comprising: decomposing the network modeled by the Cayley Digraph, which is an input, into sub inputs as pairs of permutation generators; for each pair of permutation generators, constructing the IAS; given the IAS of a pair of permutation generators, constructing a list of nodes on the IAS for which the total number of in degrees and out degrees is greater than two; checking whether the list of nodes for which the total number of in degrees and out degrees is greater than two is empty or contains one or more nodes; performing classification by (i) if the list is empty, classifying the pair of permutation generators in the class of IAS regular networks, and (ii) if the list contains one or more nodes, classifying the pair of permutation generators in the class of IAS irregular networks; assigning hamiltonian properties to the network, the assigned hamiltonian properties depending on the result of the classification; and using the hamiltonian properties to solve the decision, construction, or optimization of a hamiltonian traversal problem in the network, or to obtain an upper bound of the number of hamiltonian traversals in the network.