EvoWorkshops 2008: Applications of Evolutionary Computing pp 31-37 | Cite as
Reconstruction of Networks from Their Betweenness Centrality
Abstract
In this paper we study the reconstruction of a network topology from the values of its betweenness centrality, a measure of the influence of each of its nodes in the dissemination of information over the network. We consider a simple metaheuristic, simulated annealing, as the combinatorial optimization method to generate the network from the values of the betweenness centrality. We compare the performance of this technique when reconstructing different categories of networks –random, regular, small-world, scale-free and clustered–. We show that the method allows an exact reconstruction of small networks and leads to good topological approximations in the case of networks with larger orders. The method can be used to generate a quasi-optimal topology for a communication network from a list with the values of the maximum allowable traffic for each node.
Keywords
Simulated Annealing Betweenness Centrality Simulated Annealing Algorithm Adjacency Matrice Laplacian SpectrumPreview
Unable to display preview. Download preview PDF.
References
- 1.Barabasi, A.-L., Bonabeau, E.: Scale-free networks. Scientific American 288(5), 50–59 (2003)CrossRefGoogle Scholar
- 2.Newman, M.E.J.: The structure and function of complex networks. SIAM Review 45, 167–256 (2003)MATHCrossRefMathSciNetGoogle Scholar
- 3.Ipsen, M., Mikhailov, A.S.: Evolutionary reconstruction of networks. Phys. Rev. E. 66, 46109 (2002)CrossRefGoogle Scholar
- 4.Freeman, L.C.: A set of measures of centrality based upon betweenness. Sociometry 40, 35–41 (1977)CrossRefGoogle Scholar
- 5.Goh, K.-I., Oh, E., Jeong, H., Kahng, B., Kim, D.: Classification of scale-free networks. Proc. Natl. Acad. Sci. USA 99, 12583–12588 (2002)MATHCrossRefMathSciNetGoogle Scholar
- 6.Comellas, F., Gago, S.: Synchronizability of complex networks. J. Phys. A: Math. Theor. 40, 4483–4492 (2007)MATHCrossRefMathSciNetGoogle Scholar
- 7.Aarts, E., Lenstra, J.K. (eds.): Local Search in Combinatorial Optimization. John Wiley & Sons Ltd, New York (1997)MATHGoogle Scholar
- 8.Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220, 671–680 (1983)CrossRefMathSciNetGoogle Scholar
- 9.Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, New York (1979)MATHGoogle Scholar
- 10.Schmidt, D.C., Druffel, L.E.: A fast backtracking algorithm to test directed graphs for isomorphism using distance matrices. Journal of the ACM 23, 433–445 (1976)MATHCrossRefMathSciNetGoogle Scholar
- 11.Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998)CrossRefGoogle Scholar
- 12.Paz-Sanchez, J.: Reconstrucció de grafs a partir del grau d’intermediació (betweenness) dels seus vèrtexs. PFC (Master Thesis) (in Catalan) (July 2007)Google Scholar
- 13.Dorigo, M., Stützle, T.: Ant colony optimization. MIT Press, Cambridge (2004)MATHGoogle Scholar
- 14.Comellas, F., Sapena, E.: A multiagent algorithm for graph partitioning. In: Rothlauf, F., Branke, J., Cagnoni, S., Costa, E., Cotta, C., Drechsler, R., Lutton, E., Machado, P., Moore, J.H., Romero, J., Smith, G.D., Squillero, G., Takagi, H. (eds.) EvoWorkshops 2006. LNCS, vol. 3907, pp. 279–285. Springer, Heidelberg (2006)CrossRefGoogle Scholar
- 15.Glover, F.: Future paths for integer programming and links to artificial intelligence. Comput. & Ops. Res. 13, 533–549 (1986)MATHCrossRefMathSciNetGoogle Scholar