Complex networks on hyperbolic surfaces

Physica A: Statistical Mechanics and its Applications

Volumn 346, Issue 1-2 SPEC. ISS., 2005, Pages 20-26

  Aste, T ^a   Di Matteo, T ^a   Hyde, S T ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

Complex systems; Econophysics; Hyperbolic graphs; Networks

Indexed keywords

COMPUTATIONAL COMPLEXITY; LARGE SCALE SYSTEMS; MATHEMATICAL MODELS; RANDOM PROCESSES;

ECONOPHYSICS; HYPERBOLIC GRAPHS;

GRAPH THEORY;

EID: 9944237726     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2004.08.045     Document Type: Conference Paper

References (32)

1. L.A.N. Amaral, A. Scala, M. Barthelemy, H.E. Stanley, Proc. Natl. Acad. Sci. 97 (2000) 11149.
2. R. Albert, A. Barabási, Rev. Mod. Phys. 74 (2002) 47.
3. M.E.J. Newman, SIAM Rev. 45 (2003) 167.
4. R. Cohen, S. Havlin, Phys. Rev. Lett. 90 (2003) 058701.
5. D.J. Watts, S.H. Strogatz, Nature 393 (1998) 440-442.
6. P. Erdos, A. Rényi, Publ. Math. Inst. Hungar. Acad. Sci. 5 (1960) 17-41.
7. H.M. Ohlenbusch, T. Aste, B. Dubertret, N. Rivier, Eur. Phys. J. B 2 (1998) 211-220.
8. B. Dubertret, T. Aste, H.M. Ohlenbusch, N. Rivier, Phys. Rev. E 58 (1998) 6368-6378.
9. T. Aste, D. Sherrington, J. Phys. A 32 (1999) 7049-7956.
10. G. Ringel, Map Color Theorem, Springer, Berlin, 1974 Chapter 4.
11. P.J. Gilbin, Graphs, Surfaces and Homology, second ed., Chapman & Hall, 1981.
12. G. Ringel, J.W.T. Youngs, Proc. Nat. Acad. Sci. USA 60 (1968) 438-445.
13. T. Di Matteo, T. Aste, S.T. Hyde, S. Ramsden, preprint, 2004.
14. M. Tumminello, T. Aste, T. Di Matteo, R.N. Mantegna, 2004, in preparation.
15. J. Stillwell, Classical Topology and Combinatorial Group Theory, second ed., Springer, 1993.
16. H.S.M. Coxeter, Regular Polytopes, Dover, New York, 1973.
17. S.T. Hyde, S. Ramsden, Eur. Phys. J. B 3178 (2003) 273-284.
18. S.T. Hyde, S. Ramsden, T. Di Matteo, J.J. Longdell, Solid State Sci. 5 (2003) 35-45.
19. C.P. Bonnington, M.J. Grannell, T.S. Griggs, J. Siran, J. Comb. Theory B 78 (2000) 169-184.
20. J.W. Alexander, Ann. Math. 31 (1930) 294-322.
21. U. Pachner, Arch. Math 30 (1978) 89-91; U. Pachner, Euro. J. Comb. 12 (1991) 129-145.
22. U. Pachner, Arch. Math 30 (1978) 89-91; U. Pachner, Euro. J. Comb. 12 (1991) 129-145.
23. M.H. A Newman, R. Acad. Amsterdam 29 (1926) 610-641.
24. H.M. Ohlenbusch, T. Aste, B. Dubertret, N. Rivier, Euro. Phys. J. B 2 (1998) 211-220.
25. B. Dubertret, T. Aste, H.M. Ohlenbusch, N. Rivier, Phys. Rev. E 58 (1996) 6368-6378.
26. E. Brézin, C. Itzykson, G. Parisi, J.B. Zuber, Comm. Math. Phys. 59 (1978) 35.
27. D.V. Boulatov, V.A. Kazakov, I.K. Kostov, A.A. Migdal, Nucl. Phys. B 275 (1986) 641.
28. C. Godrèche, I. Kostov, I. Yekutieli, Phys. Rev. Lett. 69 (1992) 2674.
29. J. Bouttier, P. Di Francesco, E. Guitter, Nucl. Phys. B 675 (2003) 631.
30. T. Aste, D. Boosé, N. Rivier, Phys. Rev. E 53 (1996) 6181-6191.
31. J. Ambjorn, Y. Watabiki, Nucl. Phys. B 445 (1995) 129-142; J. Ambjorn, J. Jurkiewicz, Y. Watabiki, Nucl. Phys. B 454 (1995) 313-342.
32. J. Ambjorn, Y. Watabiki, Nucl. Phys. B 445 (1995) 129-142; J. Ambjorn, J. Jurkiewicz, Y. Watabiki, Nucl. Phys. B 454 (1995) 313-342.