MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Graph operations and synchronization of complex networks

Fatihcan M. Atay and Türker Biyikoglu


The effects of graph operations on the synchronization of coupled dynamical systems are studied. The operations range from addition or deletion of links to various ways of combining networks and generating larger networks from simpler ones. Methods from graph theory are used to calculate or estimate the eigenvalues of the Laplacian operator, which determine the synchronizability of continuous or discrete time dynamics evolving on the network. Results are applied to explain numerical observations on random, scale-free, and small-world networks. An interesting feature is that, when two networks are combined by adding links between them, the synchronizability of the resulting network may worsen as the synchronizability of the individual networks is improved.

MSC Codes:
05C50, 05C90
02.10.Ox, 05.45.Ra, 05.45.Xt, 89.75.-k
synchronization, networks, Laplacian, eigenvalue, graph operations

Related publications

2005 Repository Open Access
Fatihcan M. Atay and Türker Biyikoglu

Graph operations and synchronization of complex networks

In: Physical review / E, 72 (2005) 1.2, p. 016217