The DOI matches its Crossref record; 38 of the 38 references it cites were found in a registry or an index.
Ultrafast consensus in small-world networks
Abstract
In this paper, we demonstrate a phase transition phenomenon in algebraic connectivity of small-world networks. Algebraic connectivity of a graph is the second smallest eigenvalue of its Laplacian matrix and a measure of speed of solving consensus problems in networks. We demonstrate that it is possible to dramatically increase the algebraic connectivity of a regular complex network by 1000 times or more without adding new links or nodes to the network. This implies that a consensus problem can be solved incredibly fast on certain small-world networks giving rise to a network design algorithm for ultra fast information networks. Our study relies on a procedure called "random rewiring" due to Watts & Strogatz (Nature, 1998). Extensive numerical results are provided to support our claims and conjectures. We prove that the mean of the bulk Laplacian spectrum of a complex network remains invariant under random rewiring. The same property only asymptotically holds for scale-free networks. A relationship between increasing the algebraic connectivity of complex networks and robustness to link and node failures is also shown. This is an alternative approach to the use of percolation theory for analysis of network robustness. We also show some connections between our conjectures and certain open problems in the theory of random matrices.
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Cites
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Watts, D. J., & Strogatz, S. H. (1998) · Nature · doi:10.1038/30918 · Cited by 43,060
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Consensus Problems in Networks of Agents With Switching Topology and Time-Delays
Olfati-Saber, R., & Murray, R. M. (2004) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2004.834113 · Cited by 12,788
Self-citationCoordination of groups of mobile autonomous agents using nearest neighbor rules
Jadbabaie, A., Lin, J., & Morse, A. S. (2003) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2003.812781 · Cited by 8,339
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The Evolution of Random Graphs
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Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory
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Cited by
Consensus and Cooperation in Networked Multi-Agent Systems
Olfati-Saber, R., Fax, J. A., & Murray, R. M. (2007) · Proceedings of the IEEE · doi:10.1109/jproc.2006.887293 · Cited by 10,522
Self-citationSynchronization in complex networks
Arenas, A., Díaz-Guilera, A., Kurths, J., Moreno, Y., & Zhou, C. (2008) · Physics Reports · doi:10.1016/j.physrep.2008.09.002 · Cited by 3,713
Review on Control of DC Microgrids
Meng, L., Shafiee, Q., Ferrari Trecate, G., Karimi, H., Fulwani, D., Lu, X., & Guerrero, J. M. (2017) · IEEE Journal of Emerging and Selected Topics in Power Electronics · doi:10.1109/jestpe.2017.2690219 · Cited by 513
Distributed Consensus Algorithms in Sensor Networks: Quantized Data and Random Link Failures
Kar, S., & Moura, J. M. F. (2010) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2009.2036046 · Cited by 435
Fixed-Time Leader-Following Consensus for Second-Order Multiagent Systems With Input Delay
Ni, J., Liu, L., Liu, C., & Liu, J. (2017) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2017.2701775 · Cited by 328
Metadata
- Authors
- Olfati-Saber, R.
- Venue
- Proceedings of the 2005, American Control Conference, 2005.
- Publisher
- IEEE
- Published
- 2005-08-10
- Pages
- 2371-2378
- ISSN
- 0743-1619 (ISSN-L)
- OpenAlex
- W2124620758
- Cited by
- 384
- References
- 38
- FWCI
- 33.81
- Type
- conference paper
- Language
- en
- Open access
- closed
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