Synchronizability and connectivity of discrete complex systems
College of William and Mary
Last modified: July 27, 2006
The synchronization of discrete complex systems is critical in applications such as communication and transportation networks, neuron respiratory systems, and other systems in which either congestion can occur at individual nodes, or system wide synchrony is of importance to proper functionality. The first non-trivial eigenvalue of a network's Laplacian matrix, called the algebraic connectivity, provides a quantifiable measure of synchronizability in a network. We study the general relationship between network topology, clustering coefficient distributions, and synchronizability, as well as the effects of degree preserving rewiring on network synchronizability. In addition, we compare the synchronizability of different network topologies, including Poisson random graphs, geometric networks, preferential attachment networks, and scale-rich networks. We also explore uses of the algebraic connectivity in the design and management of complex networks where synchronization is desired (respiration networks), or detrimental to network performance (router networks).