The Analyses of Node Swapping Networks by New Graph Index

Abstract

We have proposed two new dynamic networks where two node are swapped each other, and showed that the both networks behave as a small world like in the average path length but can not make any effective discussions on the clustering coefficient because of the topological invariant properties of the networks. In this article we introduce a new index, "hamming coefficient" or "multiplicity", that can act well for these dynamic networks. The hamming coefficient or multiplicity is shown essentially to behave as the clustering coefficient in the small world network proposed by Watts and Strogatz\cite{Watt1}. By evaluating the new index, we uncover another properties of the two networks.