Department of Mathematics, Southern Illinois University Carbondale, Carbondale, IL 62901, USA
Abstract:
Imbalanced interactions or processes and directed links are often encountered in realistic networks. In this paper, we extend the well-known small-world model of Watts and Strogatz to deal with those factors. The path length and clustering properties are analyzed. Numerical results are also presented, which indicate that the extended Watts-Strogatz model may be influenced by the diversity in interaction strength.