Consensus dynamics on random rectangular graphs
Ernesto Estrada,Matthew Sheerin +1 more
TL;DR: The results prove that as the rectangle in which the nodes are embedded becomes more elongated, the RRG becomes a ’large-world’, and a poorly-connected graph, i.e., the diameter grows to infinity, and the algebraic connectivity decays to zero.
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About: This article is published in Physica D: Nonlinear Phenomena. The article was published on 01 Jun 2016. and is currently open access. The article focuses on the topics: Random geometric graph & Consensus dynamics.
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Figures
Figure 2: Change of the diameter (a) and the algebrai onne tivity (b) of RRGs with the variation in the side length of the re tangle, a. All the graphs have n = 500 nodes and the onne tion radius is r = 0.15. The squares orrespond to the average values observed for the RRG after 100 random realizations, and the ir les represents the bounds obtained by eq. 12 and eq. 11, respe tively. Noti e the semilog plot on the y-axis for the plot (b). 
Figure 4: Contour plot showing the dependen e of the time of onsensus with the onne tion radius and the re tangle side length in RRGs with 500 nodes. a) Analyti al results. b) Observed results from the simulations. The diagonal white line orresponds to the equations a = κ · r − 1.5, where κ = 28 for the analyti al and κ = 26 for the observed results. 
Figure 3: Illustration of the onsensus dynami s for a RRG with a = 1 (a) and for a = 5 (b). The simulations were arried out using a dis rete time onsensus model (see 10) with a random allo ation of initial states for the nodes. Both networks have 500 nodes and the onne tion radius is r = 0.15. Noti e that the s ale for the time axis has hanged by a fa tor of 10 from one plot to the other. ( ) Dependen e of the time for onsensus with the length of the side of the re tangle. Here the squares represent the average values of the 100 simulations and the ir les are the values obtained by the equation 21. The solid lines represent the best t whi h were obtained using 4th order polynomials. (d) Linear plot of the observed and estimated (using equation 21) for the time of onsensus of the RRGs with 500 nodes and r = 0.15.
Citations
Spectral statistics of random geometric graphs
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Spectral statistics of random geometric graphs
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Symmetric motifs in random geometric graphs
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References
Consensus and Cooperation in Networked Multi-Agent Systems
Reza Olfati-Saber,J.A. Fax,Richard M. Murray +2 more
- 05 Mar 2007
TL;DR: A theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees is provided.
Random graphs
Alan Frieze
- 22 Jan 2006
TL;DR: Some of the major results in random graphs and some of the more challenging open problems are reviewed, including those related to the WWW.
9.5K
Wireless integrated network sensors
TL;DR: The WINS network represents a new monitoring and control capability for applications in such industries as transportation, manufacturing, health care, environmental oversight, and safety and security, and opportunities depend on development of a scalable, low-cost, sensor-network architecture.
3.6K