Establishment and structure properties of the scale-free Koch network

Abstract

According the iterative algorithm of Koch curve, we generate a Koch network by considering tetrahedron as the basic unit of the iteration and investigate its structure properties, such as degree distribution, clustering coefficient, and average path length, degree correlation, analytically. The results show that the network is scale-free and the exponent of the degree distribution is γ≈332. The clustering coefficient tends to be 0870435 in the limit of large iteration and the study of the average path length proves that the network exhibits small world effect. We also find that the generated network is not degree uncorrelated because the function knn(k) is dependent on the degree of site.