Abstract
Empirical study shows that many real networks in nature and society share two generic properties: they are scale-free and they display a high degree of clustering. Quite often they are modular in nature also, implying occurrences of several small tightly linked groups which are connected in a hierarchical manner among themselves. Recently, we have introduced a model of spatial scale-free network where nodes pop-up at randomly located positions in the Euclidean space and are connected to one end of the nearest link of the existing network. It has been already argued that the large scale behaviour of this network is like the Barabási-Albert model. In the present paper we briefly review these results as well as present additional results on the study of non-trivial correlations present in this model which are found to have similar behaviours as in the real-world networks. Moreover, this model naturally possesses the hierarchical characteristics lacked by most of the models of the scale-free networks.
Similar content being viewed by others
References
A L Barabási and R Albert, Science 286, 509 (1999)
R Albert and A-L Barabási, Rev. Mod. Phys. 74, 47 (2002)
M E J Newman, SIAM Rev. 45, 167 (2003)
I Bose, in: Frontiers in biophysics edited by T P Singh and C K Dasgupta (Allied Publishers, New Delhi, 2005) p. 87
S N Dorogovtsev and J F F Mendes, Evolution of networks (Oxford University Press, 2003)
R Pastor-Satorras and A Vespigniani, Evolution and structure of internet: A statistical physics approach (Cambridge University Press, Cambridge, 2004)
M Faloutsos, P Faloutsos and C Faloutsos, Proc. ACM SIGCOMM, Comput. Commun. Rev. 29, 251 (1999)
R Pastor-Satorras, A Vazquez and A Vespignani, Phys. Rev. Lett. 87, 258701 (2001)
S H Yook, H Jeong and A-L Barabási, Proc. Natl Acad. Sci. (USA) 99, 13382 (2002)
G Mukherjee and S S Manna, Phys. Rev. E74, 036111 (2006)
D J Watts and S H Strogatz, Nature (London) 393, 440 (1998)
E Ravasz and A L Barabási, Phys. Rev. E67, 026112 (2003)
L A N Amaral, A Scala, M Barthélémy and H E Stanley, Proc. Natl Acad. Sci. (USA) 97, 11149 (2000)
A E Krause, K A Frank, D M Mason, R E Ulanowicz and W W Taylor, Nature (London) 426, 282 (2003)
M E J Newman, Phys. Rev. E64, 016131 (2001)
M A Serrano and M Boguna, Phys. Rev. E68, 015101 (R) (2003)
K Bhattacharya, G Mukherjee, J Saramki, K Kaski and S S Manna, J. Stat. Mech. P02002 (2008)
A Barrat, M Barthélémy and A Vespignani, J. Stat. Mech. P05003 (2005)
W X Wang, B H Wang, B Hu, G Yan and Q Ou, Phys. Rev. Lett. 94, 188702 (2005)
G Bianconi, Europhys. Lett. 71, 1029 (2005)
K-I Goh, B Kahng and D Kim, Phys. Rev. E72, 017103 (2005)
K Klemm and V M Eguluz, Phys. Rev. E65, 057102 (2002)
G Voronoi and J Reine, Angew. Math. 134, 198 (1908)
F Járai-Szabó and Z Néda, Physica A385, 518 (2007)
A Barrat, M Barthélémy, R Pastor-Satorras and A Vespignani, Proc. Natl Acad. Sci. (USA) 101, 3747 (2004)
S N Dorogovtsev, A V Goltsev and J F F Mendes, Phys. Rev. E65, 066122 (2002)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nandi, A.K., Mukherjee, G. & Manna, S.S. Correlations and clustering in a scale-free network in Euclidean space. Pramana - J Phys 71, 391–401 (2008). https://doi.org/10.1007/s12043-008-0173-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12043-008-0173-2