Similarity in transitions of two distinct number networks

概要

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The main objective of our study is to disclose if any network structure is hidden among the pairs of numbers obtained by splitting the consecutive integers. By adopting some preferred rule in placing the links among the pairs obtained, we have a transition from a regular to a random one through a small world one. This type of transition is also similar to the network of primes obtained by splitting the consecutive integers which indicates some general feature in both kinds of networks. We also obtained both some numerical and analytical explanations, that support the transition and also the point of transition.