Eur. Phys. J. B 74, 217-225 (2010)
https://doi.org/10.1140/epjb/e2010-00016-7

Optimal synchronization on strongly connected directed networks

CSIRO Marine and Atmospheric Research, CSIRO Centre for Complex System Science, F C Pye Laboratory - GPO Box 3023, Clunies Ross Street Canberra ACT 2601, Australia

Corresponding author: Markus.Brede@Csiro.au

Received: 19 June 2009
Revised: 6 November 2009
Published online: 21 January 2010

Abstract

In this paper we construct and analyse strongly connected sparse directed networks with an enhanced propensity for synchronization (PFS). Two types of PFS-enhanced networks are considered: (i) an eigenratio minimizing ensemble with non-vanishing complex parts of the spectrum and (ii) a class of networks with real spectrum but slightly larger eigenratios than (i). We relate the superior PFSs to a strongly skewed out-degree distribution, the density of double links and a hierarchical periphery-core organization. Ensembles (i) and (ii) are found to differ in the density of double links and the particular organization of the core and the periphery-core linkage.