Research

 

Scale-free growing networks and gravity

 

J. A. Nieto

 

Facultad de Ciencias Físico-Matemáticas de la Universidad, Autónoma de Sinaloa, 80010, Culiacán Sinaloa, México, e-mail: niet@uas.edu.mx, janieto1@asu.edu

 

Received 16 October 2012;
Accepted 17 December 2012

 

Abstract

We propose a possible relation between complex networks and gravity. Our guide in our proposal is the power-law distribution of the node degree in network theory and the information approach to gravity. The established bridge may allow us to carry geometric mathematical structures, which are considered in gravitational theories, to probabilistic aspects studied in the framework of complex networks and vice versa.

Keywords: Complex networks; gravitational theory.

 

PACS: 04.60.-m; 04.65.+e; 11.15.-q; 11.30.Ly

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

Acknowledgments

I would like to thank M. C. Marin and A. Leon for helpful comments and the Mathematical, Computational & Modeling Sciences Center of the Arizona State University for the hospitality.

 

References

1. R. Albert and A. L. Barabasi, Rev. Mod. Rhys. 74 (2002) 47.         [ Links ]

2. A. L. Barabasi, R. Albert and H. Jeong, Rhys. A 272 (1999) 173.         [ Links ]

3. R. Penrose, Angular momentum: an approach to combinatorial space-time; in Quantum theory and beyond, ed. Ted Bastin, (Cambridge University Press, 1971).         [ Links ]

4. R. Penrose and W. Rindler, Spinors and Spacetime (Cambridge University Press, 1984).         [ Links ]

5. C. Rovelli and L. Smolin, Rhys. Rev. D 52 (1995) 5743; gr-qc/9505006.         [ Links ]

6. J. C. Baez, Class. Quan. Grav. 15 (1998) 1827.         [ Links ]

7. R. Gambini, J. Lewandowski, D. Marolf and J. Pullin, Int. J. Mod. Rhys. D 7 (1998) 97; gr-qc/9710018.         [ Links ]

8. R. Gambini, J. Griego and J. Pullin, Rhys. Lett. B 413 (1997) 260; gr-qc/9703042.         [ Links ]

9. J. M. García-Islas, Class. Quant. Grav. 21 (2004) 445; gr-qc/0307054.         [ Links ]

10. E. P. Verlinde, JHER 1104 (2011) 029; arXiv:1001.0785 [hep-th]         [ Links ].

11. S.N. Dorogovtsev, J. F. F. Mendes, and A. N. Samukhin, Rhys. Rev. E 63 (2001)062101.         [ Links ]

12. S. N. Dorogovtsev, J. F. F. Mendes, A. M. Povolotsky, and A. N. Samukhin, Rhys. Rev. Lett. 95 (2005) 19570; cond-mat/0505193.         [ Links ]

13. S. N. Dorogovtsev, J. F. F. Mendes, and A. N. Samukhin, Rhys. Rev. Lett. 85 (2000) 4633.         [ Links ]

14. P. L. Krapivsky, S. Redner, and F. Leyvraz, Rhys. Rev. Lett. 85 (2000) 4629.         [ Links ]

15. M. Dehmer, Appl. Math. Com. 201 (2008) 82.         [ Links ]

16. A. Björner, M. Las Vergnas, B. Sturmfels, N. White and G. M. Ziegler, Oriented Matroids (Cambridge University Press, Cambridge, 1999).         [ Links ]

17. J. A. Nieto, Adv. Theor. Math. Rhys. 8 (2004) 177; hep-th/0310071.         [ Links ]

18. J. A. Nieto, Adv. Theor. Math. Rhys. 10 (2006) 747; hep-th/0506106.         [ Links ]

19. H. Whitney, Trans. Am. Math. Soc. 34 (1932) 339.         [ Links ]

20. H. Whitney, Am. J. of Math. 57 (1935) 509.         [ Links ]

21. J. A. Nieto, Rev. Mex. Fis. 57 (2011) 400. arXiv:1003.4750.         [ Links ]

22 . A. Ashtekar and J. Lewandowski, Class. Quan. Grav. 21 (2004) R53.         [ Links ]