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Synchronization Phenomena on Networks

  • Reference work entry
Computational Complexity

  • 241 Accesses

Article Outline

Glossary

Definition of the Subject

Introduction

Basic Concepts of Network Synchronization

Synchronizability Versus Structure

Enhancing Network Synchronizability

Future Research Outlook

Acknowledgments

Bibliography

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Abbreviations

Synchronization:

A problem in time‐keeping, requiring the coordination of events to operate a system or a task in unison.

Distance:

A measure between two nodes, defined as the number of edges connecting them through the shortest paths.

Average distance:

The mean distance, averaged over all pairs of nodes on the network.

Clustering coefficient:

The probability that two randomly‐selected neighboring nodes of a node are directly connected each other.

Node‐degree:

The number of edges incident from a node.

Random‐graph network:

A type of graph obtained by starting with a set of nodes and then adding edges between them at random.

Small‐world network:

A type of graph in which most nodes are not neighbors of each other, but most nodes can be reached from any other node by a small number of connection steps; thus, a small‐world network is highly clustered like a regular graph, and yet with a small average distance, just like a random graph.

Scale‐free network:

A type of graph in which a small number of nodes have a large number of connections while a large number of nodes have a small number of connections, whose node‐degree distribution typically follows a power‐law form, with both structure and dynamics being independent of the network size.

Node‐betweenness:

A measure of the extent to which a given node is occupied by the amount of information passing through it via shortest paths between other nodes, namely, the portion of shortest paths between all pairs of nodes which have data traffic going through this particular node in the network.

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Acknowledgments

The authors thank the American Physics Society and the Elsevier Publisher for their permission to use some of their publishedsimulation figures, which have all been referenced (in the figure captions). The authors also thank Dr. Jian-Guo Liu for his helpful commentsand suggestions. G.R.C. was supported by the NSFC/RGC joint research scheme under grant N‑CityU107/07.B.H.W. was supported by the NNSFCunder Grants 10472116 and A0524701, and the Specialized Program under the Presidential Funds of CAS. T.Z. was supported by NNSFC under Grants10635040 and 70471033.

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Authors and Affiliations

  1. Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China

    Guanrong Chen

  2. Department of Modern Physics and Nonlinear Science Center, University of Science and Technology of China, Hefei Anhui, China

    Ming Zhao, Tao Zhou & Bing-Hong Wang

  3. Institute of Complex Adaptive Systems, Shanghai Academy of System Science, Shanghai, China

    Bing-Hong Wang

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  1. Guanrong Chen
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  2. Ming Zhao
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  3. Tao Zhou
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Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Chen, G., Zhao, M., Zhou, T., Wang, BH. (2012). Synchronization Phenomena on Networks. In: Meyers, R. (eds) Computational Complexity. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1800-9_196

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