Static and dynamic properties of small-world connection topologies based on transit-stub networks

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 propertiesmore 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.We thank the MCyT (BFI 2000-015). (RH) was also funded by DE-FG03-96ER14092 and (CA) was supported by ARO-MURI grant DAA655-98-1-0249 during a four month stay at UCSD. We also thank Lev Trimsing for useful discussion