MiS Preprint Repository
We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) 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.
Network synchronization: Spectral versus statistical properties
Fatihcan M. Atay, Türker Biyikoglu and Jürgen JostAbstract
We consider synchronization of weighted networks, possibly with asymmetrical connections. Focusing on causal relations rather than the observed correlations, we show that the synchronizability of networks cannot be directly inferred from their statistical properties. Small local changes in the network structure can sensitively affect the eigenvalues relevant for synchronization, while the gross statistical network properties remain essentially unchanged. Consequently, commonly used statistical properties, including the degree distribution, degree homogeneity, average degree, average distance, degree correlation and clustering coefficient, can fail to characterize the synchronizability of networks in terms of causal relations, despite the observed correlations.
- Received:
- 24.10.06
- Published:
- 24.10.06
- PACS:
- 02.10.Ox, 05.45.Ra, 05.45.Xt, 89.75
- Keywords:
- synchronization, graph, degree distribution, algebraic connectivity