Abstract
The hierarchical organization in complex networks is investigated from the point of view of nearest neighbor correlation. By plotting the mean total degree of the nearest neighbors versus degree of the given node, more than one linear branches will be observed for hierarchical network. An example of hierarchical network with 1-hub-4-peripheral is constructed for illustrative purpose and real data on the World Wide Web and AS Internet are analyzed for comparison. Two branches are clearly observed for the total degree of neighbors of the World Wide Web, indicative of the existence of hierarchical organization and the result is consistent with the analysis based on local clustering coefficient. Only one branch is observed for the AS Internet data set, but the result is not conclusive as the size of the data set is not sufficiently large. The total degree of nearest neighbor provides a good complementary test to the existing method based on the local clustering coefficients.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. L. Barabási and R. Albert, Science 286, 509 (1999).
C. W. Ma and K. Y. Szeto, Phys. Rev. E 73, 047101 (2006).
D. A. Aboav, Metallography 3, 383 (1970); ibid, 13, 43 (1980).
D. J. Watts and S.H. Strogatz, Nature 393, 440 (1998).
D. Weaire, Metallography 7, 157 (1974).
E. Ravasz, A. L. Somera, D. A. Mongru, Z. N. Oltvai, A.-L. Barabasi, Science 297, 1551 (2002).
E. Ravasz and A.-L. Barabasi, Phys. Rev. E 67, 026112 (2003).
M. Newman: http://www-personal.umich.edu/~mejn/netdata/ , (unpublished).
P. Erdos and A. Renyi, On random graphs, Publ. Math. Debrecen, 6 (1959), pp. 290–297.
Q. Chen, H. Chang, R. Govindan, S. Jamin, S. J. Shenker, and W. Willinger, The origin of power laws in Internt topologies revisited, in Proceedings of the 21st Annual Joint Conference of the IEEE Computer and Communications Societies, IEEE Computer Society, Los Alamitos, CA, (2002).
R. Albert and A.-L. Barabasi, Rev. Mod. Phys. 74, 47 (2002), and references therein.
R. Albert, H. Jeong, and A.-L. Barabasi, Nature 401, 130 (1999).
R. Albert, H. Jeong, and A.-L. Barabasi, Nature 406, 378 (2000).
R. Cohen, K. Erez, D. ben Avraham, and S. Havlin, Phys. Rev. Lett. 86, 3682 (2001).
R. Pastor-Satorras and A. Vespignani, Phys. Rev. Lett. 86, 3200 (2001).
S. H. Strogatz and D. J. Watts, Science 296, 1302 (2002).
S. H. Strogatz, Nature 410, 268–276 (2001).
Z. Z. Guo and Kwok Yip Szeto, Phys. Rev. E 71, 066115 (2005).
Z. Z. Guo, K. Y. Szeto, and Xiujun Fu, Phys. Rev. E 70, 016105 (2004).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Wang, C.L., Au, K.W., Chan, C.K., Lau, H.W., Szeto, K.Y. (2008). Detecting Hierarchical Organization in Complex Networks by Nearest Neighbor Correlation. In: Krasnogor, N., Nicosia, G., Pavone, M., Pelta, D. (eds) Nature Inspired Cooperative Strategies for Optimization (NICSO 2007). Studies in Computational Intelligence, vol 129. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78987-1_44
Download citation
DOI: https://doi.org/10.1007/978-3-540-78987-1_44
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78986-4
Online ISBN: 978-3-540-78987-1
eBook Packages: EngineeringEngineering (R0)