Approximating the largest eigenvalue of the modified adjacency matrix of networks with heterogeneous node biases

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 79, Issue 5, 2009, Pages

  Ott, Edward ^a   Pomerance, Andrew ^a  

^a UNIVERSITY OF MARYLAND   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADJACENCY MATRICES; ANALYTIC APPROXIMATION; ANTICORRELATION; BOOLEAN MODEL; COMMUNITY STRUCTURES; DIRECTED NETWORK; DYNAMICAL BEHAVIORS; EIGEN-VALUE; EIGENVALUE PROBLEM; GENE NETWORKS; HETEROGENEOUS NODES; LARGEST EIGENVALUE; MATRIX Q; MEAN-FIELD; NETWORK LINKS; NETWORK SYSTEMS; NUMERICAL EXPERIMENTS; Q-VALUE;

HETEROGENEOUS NETWORKS; SOLVENTS;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 67549118625     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.79.056111     Document Type: Article

References (15)

1. M. E. J. Newman, Phys. Rev. Lett. 89, 208701 (2002). 10.1103/PhysRevLett. 89.208701
2. J. G. Restrepo, E. Ott, and B. R. Hunt, Phys. Rev. E 76, 056119 (2007). 10.1103/PhysRevE.76.056119
3. This definition of ρ appears in Ref.. Newman characterized assortativity using a different quantity, but Eq. 2 is more relevant for our purposes.
4. M. Girvan and M. E. J. Newman, Proc. Natl. Acad. Sci. U.S.A. 99, 7821 (2002). 10.1073/pnas.122653799
5. For example, see S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang, Phys. Rep. 424, 175 (2006) 10.1016/j.physrep.2005.10.009
6. L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 80, 2109 (1998). 10.1103/PhysRevLett.80.2109
7. J. G. Restrepo, E. Ott, and B. R. Hunt, Phys. Rev. E 71, 036151 (2005). 10.1103/PhysRevE.71.036151
8. E. Ott, P. So, E. Barreto, and T. M. Antonsen, Physica D 173, 29 (2002) 10.1016/S0167-2789(02)00663-2
9. J. G. Restrepo, E. Ott, and B. R. Hunt, Phys. Rev. Lett. 96, 254103 (2006). 10.1103/PhysRevLett.96.254103
10. A. Pomerance, E. Ott, M. Girvan, and W. Losert, Proc. Natl. Acad. Sci. U.S.A. 106, 8209 (2009). 10.1073/pnas.0900142106
11. J. G. Restrepo, E. Ott, and B. R. Hunt, Phys. Rev. Lett. 100, 058701 (2008). 10.1103/PhysRevLett.100.058701
12. R. Cohen, K. Erez, D. ben-Avraham, and S. Havlin, Phys. Rev. Lett. 85, 4626 (2000). 10.1103/PhysRevLett.85.4626
13. Y. Moreno, R. Pastor-Satorras, and A. Vespignani, Eur. Phys. J. B 26, 521 (2002). 10.1140/epjb/e20020122
14. A. Vazquez and Y. Moreno, Phys. Rev. E 67, 015101 (R) (2003). 10.1103/PhysRevE.67.015101
15. M. Boguñá and R. Pastor-Satorras, Phys. Rev. E 66, 047104 (2002). 10.1103/PhysRevE.66.047104