Analysis of Synchronizability in Small-World Complex Networks

The research Zambrano-Serrano, E. related to Posadas-Castillo, C. complex networks Platas-Garza, M.A. is an active field mainly inspired by its broad ability to model a wide variety of Rodríguez-Cruz, J.R. systems. For instance, we observe biological networks at the microscopic level, genetic regulation networks, protein networks, and neural networks. On the other hand, we find computer networks and social networks at a higher level of organization. For this reason, the study of complex networks is attractive, specifically those that present small-world characteristics and nonlinear dynamic systems at their nodes. This chapter presents a comparison of three algorithms for generating small-world complex networks, Watts–Strogatz, Newman–Watts, and Sanchez–Posadas, intending to show which algorithm enhances the synchrony of complex networks that consider chaotic oscillators in their nodes, from the perspective of synchronizability—the capacity of networks in synchronizing the activity of their dynamical parts. The comparison of these algorithms has been made from the eigenratio of the Laplacian matrix from the connection graph. It relates the largest eigenvalue divided by the second smallest one. The results that show the proposed by Sanchez–Posadas algorithm exhibit certain advantages over the other two studied.