Open AccessEstablishment and structure properties of the scale-free Koch network
Author(s) -
Liu Jia-Xue,
Xiangbin Kong
Publication year - 2010
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.59.2244
Subject(s) - degree (music) , degree distribution , clustering coefficient , exponent , scale free network , average path length , cluster analysis , scale (ratio) , path (computing) , statistical physics , function (biology) , path length , complex network , mathematics , computer science , physics , statistics , combinatorics , shortest path problem , graph , computer network , linguistics , philosophy , quantum mechanics , evolutionary biology , biology , acoustics , programming language
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≈332. The clustering coefficient tends to be 0870435 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.