Complex Systems

Static and Dynamic Properties of Small-world Connection Topologies Based on Transit-stub Networks Download PDF

Carlos Aguirre
Computer Engineering Department,
Universidad Autónoma de Madrid,
28049 Madrid, Spain

Fernando Corbacho
Computer Engineering Department,
Universidad Autónoma de Madrid,
28049 Madrid, Spain

Ramón Huerta
Computer Engineering Department,
Universidad Autónoma de Madrid,
28049 Madrid, Spain
and
Institute of Nonlinear Science
University of California
San Diego, La Jolla, CA 92093-0402

Abstract

Many real complex networks are believed to belong to a class called small-world (SW) networks. SW networks are graphs with high local clustering and small distances between nodes. A standard approach to constructing SW networks consists of varying the probability of rewiring each edge on a regular graph. As the initial substrate for the regular graph some specific topologies are usually selected such as ring-lattices or grids. However, these regular graphs are not suitable for modeling certain hierarchical topologies. A new regular substrate is proposed in this paper. The proposed substrate resembles topologies with certain hierarchical properties more accurately. Then, different dynamics inspired by networking protocols are used to characterize dynamical properties of a network. Measuring transmission times and error rates lead us to consider networks with SW features as the most reliable and fastest, regardless of the routing policies.