Synchronization properties of network motifsI. Lodato1, S. Boccaletti2 and V. Latora3
1 Scuola Superiore di Catania - Via S. Paolo 73, 95123 Catania, Italy
2 CNR- Istituto dei Sistemi Complessi - Via Madonna del Piano 10, 50019 Sesto Fiorentino (FI), Italy
3 Dipartimento di Fisica e Astronomia, Università di Catania, and INFN - Via S. Sofia 64, 95123 Catania, Italy
received 7 November 2006; accepted in final form 26 February 2007; published April 2007
published online 22 March 2007
We address the problem of understanding the variable abundance of 3-node and 4-node subgraphs (motifs) in complex networks from a dynamical point of view. As a criterion in the determination of the functional significance of a n-node subgraph, we propose an analytic method to measure the stability of the synchronous state (SSS) the subgraph displays. We show that, for undirected graphs, the SSS is correlated with the relative abundance, while in directed graphs the correlation exists only for some specific motifs.
89.75.-k - Complex systems.
05.45.Xt - Synchronization; coupled oscillators.
87.18.Sn - Neural networks.
© Europhysics Letters Association 2007