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Random matrix theory approach to complex networks

Grant number: 19/06931-2
Support Opportunities:Research Grants - Visiting Researcher Grant - International
Start date: September 01, 2019
End date: April 10, 2020
Field of knowledge:Physical Sciences and Mathematics - Physics - General Physics
Principal Investigator:Francisco Aparecido Rodrigues
Grantee:Francisco Aparecido Rodrigues
Visiting researcher: José Antonio Méndez-Bermúdez
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

In this Project we pretend to introduce and characterize null models, based on random matrix ensembles, for complex networks of current interest. In particular we plan to study: (i) random networks with gain and/or loss, (ii) non-uniform random regular graphs, (iii) bipartite networks, (iv) mutualistic networks, and (v) directed networks. We will perform a scaling analysis to define the universal parameter of each null model, i.e., the parameter that fixes the properties of the cor- responding network model. To this end we will compute quantities commonly used in Random Matrix Theory studies, such as: (i) the nearest- neighbor energy-level spacing distribution, (ii) the distribution of the ratios between nearest-neighbor energy-level spacings, (iii) the average ratio between nearest-neighbor energy-level spacings, (iv) the average Shannon entropy (or average information entropy) of the eigenvectors, and (v) the in- verse participation ratio of the eigenvectors. In all cases we will identify the metallic phase (where the eigenvectors of the null model are extended; so the corresponding network is highly connected), the isolating phase (where the eigenvectors of the null model are localized; so the corresponding network is almost disconnected), as well as the transition regime between both phases. Whenever possible, we will validate our results with data from real-world networks. (AU)

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Scientific publications (22)
(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)
HERRERA-GONZALEZ, I. F.; MENDEZ-BERMUDEZ, J. A.. Heat conduction in harmonic chains with Levy-type disorder. Physical Review E, v. 100, n. 5, . (19/06931-2)
PERON, THOMAS; DE RESENDE, BRUNO MESSIAS F.; RODRIGUES, FRANCISCO A.; COSTA, LUCIANO DA F.; MENDEZ-BERMUDEZ, J. A.. Spacing ratio characterization of the spectra of directed random networks. Physical Review E, v. 102, n. 6, . (13/07375-0, 16/23827-6, 15/22308-2, 19/06931-2, 16/25682-5)
AGUILAR-SANCHEZ, R.; MENDEZ-BERMUDEZ, J. A.; RODRIGUES, FRANCISCO A.; SIGARRETA, JOSE M.. Topological versus spectral properties of random geometric graphs. Physical Review E, v. 102, n. 4, . (19/06931-2)
PINEDA-PINEDA, JAIR J.; MARTINEZ-MARTINEZ, C. T.; MENDEZ-BERMUDEZ, J. A.; MUNOZ-ROJAS, JESUS; SIGARRETA, JOSE M.. Application of Bipartite Networks to the Study of Water Quality. SUSTAINABILITY, v. 12, n. 12, . (19/06931-2)
MARTINEZ-MARTINEZ, C. T.; MENDEZ-BERMUDEZ, J. A.; RODRIGUEZ, JOSE M.; SIGARRETA, JOSE M.. Computational and Analytical Studies of the Harmonic Index on Erdos-Renyi Models. MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, v. 85, n. 2, p. 395-426, . (19/06931-2)
MARTINEZ-MARTINEZ, C. T.; MENDEZ-BERMUDEZ, J. A.; RODRIGUEZ, JOSE M.; SIGARRETA, JOSE M.. Computational and analytical studies of the Randic index in Erdos-Renyi models. Applied Mathematics and Computation, v. 377, . (19/06931-2)
MORENO-RODRIGUEZ, L. A.; IZRAILEV, F. M.; MENDEZ-BERMUDEZ, J. A.. PT-symmetric tight-binding model with asymmetric couplings. Physics Letters A, v. 384, n. 21, . (19/06931-2)
RAZO-LOPEZ, L. A.; FERNANDEZ-MARIN, A. A.; MENDEZ-BERMUDEZ, J. A.; SANCHEZ-DEHESA, J.; GOPAR, V. A.. Delay time of waves performing Levy walks in 1D random media. SCIENTIFIC REPORTS, v. 10, n. 1, . (19/06931-2)
CARRERA-NUNEZ, M.; MARTINEZ-ARGUELLO, A. M.; MENDEZ-BERMUDEZ, J. A.. Multifractal dimensions and statistical properties of critical ensembles characterized by the three classical Wigner-Dyson symmetry classes. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 573, p. 13-pg., . (19/06931-2)
PERON, THOMAS; DE RESENDE, BRUNO MESSIAS F.; RODRIGUES, FRANCISCO A.; COSTA, LUCIANO DA F.; MENDEZ-BERMUDEZ, J. A.. Spacing ratio characterization of the spectra of directed random networks. PHYSICAL REVIEW E, v. 102, n. 6, p. 9-pg., . (19/06931-2, 16/25682-5, 16/23827-6, 13/07375-0, 15/22308-2)
HERRERA-GONZALEZ, I. F.; MENDEZ-BERMUDEZ, J. A.. Heat conduction in harmonic chains with Levy-type disorder. PHYSICAL REVIEW E, v. 100, n. 5, p. 8-pg., . (19/06931-2)
DE OLIVEIRA, JULIANO A.; PERRE, RODRIGO M.; MENDEZ-BERMUDEZ, J. A.; LEONEL, EDSON D.. Leaking of orbits from the phase space of the dissipative discontinuous standard mapping. Physical Review E, v. 103, n. 1, . (18/14685-9, 19/06931-2, 19/14038-6)
ALONSO, L.; MENDEZ-BERMUDEZ, J. A.; ESTRADA, ERNESTO. Geometrical and spectral study of beta-skeleton graphs. Physical Review E, v. 100, n. 6, . (19/06931-2)
TORRES-VARGAS, G.; FOSSION, R.; MENDEZ-BERMUDEZ, J. A.. Normal mode analysis of spectra of random networks. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 545, . (19/06931-2)
HERRERA-GONZALEZ, I. F.; MENDEZ-BERMUDEZ, J. A.. Controlling the size scaling of the thermal conductivity in harmonic chains with correlated mass disorder. Physics Letters A, v. 384, n. 18, . (19/06931-2)
AGUILAR-SANCHEZ, R.; MENDEZ-BERMUDEZ, J. A.; RODRIGUES, FRANCISCO A.; SIGARRETA, JOSE M.. Topological versus spectral properties of random geometric graphs. PHYSICAL REVIEW E, v. 102, n. 4, p. 8-pg., . (19/06931-2)
PERRE, RODRIGO M.; CARNEIRO, BARBARA P.; MENDEZ-BERMUDEZ, J. A.; LEONEL, EDSON D.; DE OLIVEIRA, JULIANO A.. On the dynamics of two-dimensional dissipative discontinuous maps. CHAOS SOLITONS & FRACTALS, v. 131, . (18/14685-9, 17/14414-2, 19/06931-2, 14/18672-8)
ALONSO, L.; MENDEZ-BERMUDEZ, J. A.; ESTRADA, ERNESTO. Geometrical and spectral study of beta-skeleton graphs. PHYSICAL REVIEW E, v. 100, n. 6, p. 8-pg., . (19/06931-2)
AGUILAR-SANCHEZ, R.; HERRERA-GONZALEZ, I. F.; MENDEZ-BERMUDEZ, J. A.; SIGARRETA, JOSE M.. Computational Properties of General Indices on Random Networks. SYMMETRY-BASEL, v. 12, n. 8, . (19/06931-2)
AGUILAR-SANCHEZ, R.; MENDEZ-BERMUDEZ, J. A.; RODRIGUEZ, JOSE M.; SIGARRETA, JOSE M.. Analytical and statistical studies of Rodriguez-Velazquez indices. JOURNAL OF MATHEMATICAL CHEMISTRY, v. 59, n. 5, . (19/06931-2)
DE OLIVEIRA, JULIANO A.; PERRE, RODRIGO M.; MENDEZ-BERMUDEZ, J. A.; LEONEL, EDSON D.. Leaking of orbits from the phase space of the dissipative discontinuous standard mapping. PHYSICAL REVIEW E, v. 103, n. 1, p. 6-pg., . (19/14038-6, 18/14685-9, 19/06931-2)
DA COSTA, DIOGO RICARDO; PALMERO, MATHEUS S.; MENDEZ-BERMUDEZ, J. A.; IAROSZ, KELLY C.; SZEZECH JR, JOSE D.; BATISTA, ANTONIO M.. Tilted-hat mushroom billiards: Web-like hierarchical mixed phase space. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 91, p. 9-pg., . (19/06931-2, 18/03000-5, 20/02415-7, 15/07311-7, 18/03211-6)