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The Scientific World Journal
Volume 2014, Article ID 759391, 8 pages
Research Article

Geometric Assortative Growth Model for Small-World Networks

1Singapore University of Technology and Design, Singapore 138682
2Institute for Cyber Security, University of Texas at San Antonio, TX 78249, USA

Received 8 August 2013; Accepted 21 October 2013; Published 23 January 2014

Academic Editors: H. M. Chamberlin and Y. Zhang

Copyright © 2014 Yilun Shang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


It has been shown that both humanly constructed and natural networks are often characterized by small-world phenomenon and assortative mixing. In this paper, we propose a geometrically growing model for small-world networks. The model displays both tunable small-world phenomenon and tunable assortativity. We obtain analytical solutions of relevant topological properties such as order, size, degree distribution, degree correlation, clustering, transitivity, and diameter. It is also worth noting that the model can be viewed as a generalization for an iterative construction of Farey graphs.