Network synchronization: Optimal and Pessimal Scale-Free Topologies

Details Network synchronization: Optimal and Pessimal Scale-Free Topologies Network synchronization: Optimal and Pessimal Scale-Free Topologies

2007-10-25

arxiv.org/abs/0710.4886v1

J. Phys. A 41, 224008 (2008)

Physics

Condensed Matter

Disordered Systems and Neural Networks

11 pages, 4 figs, submitted to J. Phys. A (proceedings of Complex Networks 2007)

Scientific paper

10.1088/1751-8113/41/22/224008

By employing a recently introduced optimization algorithm we explicitely design optimally synchronizable (unweighted) networks for any given scale-free degree distribution. We explore how the optimization process affects degree-degree correlations and observe a generic tendency towards disassortativity. Still, we show that there is not a one-to-one correspondence between synchronizability and disassortativity. On the other hand, we study the nature of optimally un-synchronizable networks, that is, networks whose topology minimizes the range of stability of the synchronous state. The resulting ``pessimal networks'' turn out to have a highly assortative string-like structure. We also derive a rigorous lower bound for the Laplacian eigenvalue ratio controlling synchronizability, which helps understanding the impact of degree correlations on network synchronizability.

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