Complex networks: a random matrix approach

• Grant number: 14/25997-0
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: February 20, 2015
• End date: April 19, 2015
• Field of knowledge: Physical Sciences and Mathematics - Physics - Condensed Matter Physics
• Principal Investigator: Francisco Aparecido Rodrigues
• Grantee: Francisco Aparecido Rodrigues
• Visiting researcher: Jose Antonio Mendez-Bermudez
• Visiting researcher institution: Benemérita Universidad Autónoma de Puebla (BUAP), Mexico
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Since complex networks present random organization, there is an interesting association between complex networks and random matrix theory (RMT). Indeed, several works have shown that RMT formalism can be considered to identify universal properties of networks. Despite the contribution of the early works, several questions are still open regarding the application of RMT to complex networks. In this way, the objective of the current project aims at the study of spectral, eigenfunction, and transport properties of disordered networks using RMT concepts. We are interested in the analysis of the spectral and eigenfunction properties of the adjacency and Laplacian matrices of networks. These investigations will be developed by considering numerical and analytical treatments. The studies prosed here will complement early works on random matrix analysis of networks and yield new research topics, which will contribute to reinforce the collaboration between the Complex Systems Group (at Instituto de Fisica, Benemerita Universidad Autonona de Puebla) and the Complex Systems, Particles and Control Group (at the Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo). (AU)

Scientific publications

(5)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

MENDEZ-BERMUDEZ, J. A.; MARTINEZ-MENDOZA, A. J.; LIVORATI, ANDRE L. P.; LEONEL, EDSON D.. Leaking of trajectories from the phase space of discontinuous dynamics. Journal of Physics A-Mathematical and Theoretical, v. 48, n. 40, OCT 9 2015. (14/25997-0, 13/14655-9, 12/23688-5, 14/25316-3)

MENDEZ-BERMUDEZ, J. A.; MARTINEZ-MENDOZA, A. J.; GOPAR, V. A.; VARGA, I.. Lloyd-model generalization: Conductance fluctuations in one-dimensional disordered systems. PHYSICAL REVIEW E, v. 93, n. 1, p. 5-pg., 2016-01-20. (14/25997-0)

MENDEZ-BERMUDEZ, J. A.; MARTINEZ-MENDOZA, A. J.; GOPAR, V. A.; VARGA, I.. Lloyd-model generalization: Conductance fluctuations in one-dimensional disordered systems. Physical Review E, v. 93, n. 1, JAN 20 2016. (14/25997-0)

MENDEZ-BERMUDEZ, J. A.; DE OLIVEIRA, JULIANO A.; AGUILAR-SANCHEZ, R.; LEONEL, EDSON D.. Scaling properties for a family of discontinuous mappings. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 436, p. 943-951, OCT 15 2015. (12/23688-5, 14/25997-0, 13/14655-9, 14/18672-8)

MENDEZ-BERMUDEZ, J. A.; DE OLIVEIRA, JULIANO A.; LEONEL, EDSON D.. Analytical description of critical dynamics for two-dimensional dissipative nonlinear maps. Physics Letters A, v. 380, n. 22-23, p. 1959-1963, MAY 20 2016. (12/23688-5, 14/25997-0, 13/14655-9, 14/18672-8)