Perturbation results for the Estrada index in weighted networks

The logarithm of the Estrada index has been proposed recently as a spectral measure to character efficiently the robustness of complex networks. In this paper, we explore the Estrada index in weighted networks and develop various perturbation results based on spectral graph theory. It is shown that the robustness of a network may be enhanced even when some edge weights are reduced. This is of particular theoretical and practical significance to network design and optimization.

[1]  J. A. Rodríguez-Velázquez,et al.  Subgraph centrality in complex networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  J. A. Rodríguez-Velázquez,et al.  Spectral measures of bipartivity in complex networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  S. Serra-Capizzano.  Jordan Canonical Form of the Google Matrix: A Potential Contribution to the PageRank Computation , 2005 .

[4]  D. Cvetkovic,et al.  Spectra of Graphs: Theory and Applications , 1997 .

[5]  Bojan Mohar,et al.  Isoperimetric numbers of graphs , 1989, J. Comb. Theory, Ser. B.

[6]  A. Brauer.  Limits for the characteristic roots of a matrix. IV: Applications to stochastic matrices , 1952 .

[7]  Robustness of Random Graphs Based on Natural Connectivity , 2010, 1009.3430.

[8]  N. Biggs.  Algebraic Graph Theory: COLOURING PROBLEMS , 1974 .

[9]  Gunter Bolch,et al.  Analytical approach to discrete optimization of queueing networks , 1990, Comput. Commun..

[10]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[11]  Ernesto Estrada.  Characterization of 3D molecular structure , 2000 .

[12]  M. Fiedler.  Algebraic connectivity of graphs , 1973 .

[13]  H. A. Jung,et al.  On a class of posets and the corresponding comparability graphs , 1978, J. Comb. Theory B.

[14]  M. Krishnamoorthy,et al.  Fault diameter of interconnection networks , 1987 .

[15]  J. A. Peña,et al.  Estimating the Estrada index , 2007 .

[16]  Wu Jun,et al.  Natural Connectivity of Complex Networks , 2010 .