Lack of Gromov-hyperbolicity in colored random networks

Panamerican Mathematical Journal

Volumn 21, Issue 1, 2011, Pages 27-36

  Shang, Yilun ^a  

^a UNIVERSITY OF TEXAS AT SAN ANTONIO   (United States)

Author keywords

Complex network; Hyperbolicity; Random graph

Indexed keywords

EID: 79959439238     PISSN: 10649735     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (15)

1. S. Arnborg, J. Lagergren and D. Seese, Easy problems for tree-decomposable graphs. J. Algorithms, 12 (1991) 308-340.
2. B. Bollobás, Random Graphs. Cambridge University Press, New York (2001).
3. M. Brisdon and A. Haefliger, Metric Spaces of Non-positive Curvature. Springer, New York (1991).
4. A. Dress, B. Holland, K. T. Huber, J. H. Koolen, V. Moulton and J. Weyer-Menkhoff, δ additive and δ ultra-additive maps, Gromov's trees, and the Farris transform. Discrete Appl. Math., 146 (2005) 51-73. (Pubitemid 40142466)
5. A. Dress, K. T. Huber and V. Moulton, Some uses of the Farris transform in mathematics and phylogenetics: a review. Ann. Combina., 11 (2007) 1-37.
6. M. Gromov, Hyperbolic groups, In: Essays in Group Theory. Springer, New York (1987) 75-263.
7. M. Gromov, Metric Structures for Riemannian and Non-Riemannian Spaces. Springer, New York (2001).
8. E. Jonckheere and P. Lohsoonthorn, Geometry of network security. Proc. American Control Conference, 2004, 976-981.
9. E. Jonckheere and P. Lohsoonthorn, A hyperbolic geometry approach to multi-path routing. Proc. 10th Mediterranean Conf. on Control and Automation, 2002, FA5-1.
10. E. Jonckheere, M. Lou, J. Hespanha and P. Barooah, Effective resistance of Gromov-hyperbolic graphs: application to asymptotic sensor network problems. Proc. 46th IEEE Conference on Decision and Control, 2007, 1453-1458.
11. D. Krioukov, F. Papadopoulos, M. Kitsak, A. Vahdat and M. Boguñá, Hyperbolic geometry of complex networks. Phys. Rev. E, 82 (2010) 036106.
12. O. Narayan and I. Saniee, The large scale curvature of networks. arXiv:0907.1478 (2009).
13. O. Narayan, I. Saniee and G. H. Tucci, Lack of spectral gap and hyperbolicity in asymptotic Erdos-Rényi random graphs. arXiv: 1009.5700 (2010).
14. M. Porfiri, D. J. Stilwell, E. M. Bollt and J. D. Skufca, Random talk: random walk and synchronizability in a moving neighborhood network. Physica D, 224 (2006) 102-113. (Pubitemid 44751215)
15. Y. Shang, Multi-agent coordination in directed moving neighbourhood random networks. Chin. Phys. B, 19 (2010) 070201.