Random matrix theory approach to complex networks

• Grant number: 19/06931-2
• Support type: Research Grants - Visiting Researcher Grant - International
• Duration: September 01, 2019 - April 10, 2020
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal researcher: Francisco Aparecido Rodrigues
• Grantee: Francisco Aparecido Rodrigues
• Visiting researcher: José Antonio Méndez-Bermúdez
• Visiting researcher institution: Benemérita Universidad Autónoma de Puebla (BUAP), Mexico
• Home 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)

Scientific publications

(15)

(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)

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 MAR 2021. Web of Science Citations: 0.

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 JAN 13 2021. Web of Science Citations: 0.

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, 2021. Web of Science Citations: 1.

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 DEC 10 2020. Web of Science Citations: 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 NOV 30 2020. Web of Science Citations: 0.

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 OCT 16 2020. Web of Science Citations: 0.

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 AUG 2020. Web of Science Citations: 0.

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 JUL 27 2020. Web of Science Citations: 0.

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, JUL 15 2020. Web of Science Citations: 0.

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 JUN 26 2020. Web of Science Citations: 0.

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 JUN 2020. Web of Science Citations: 0.

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, MAY 1 2020. Web of Science Citations: 1.

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, FEB 2020. Web of Science Citations: 0.

ALONSO, L.; MENDEZ-BERMUDEZ, J. A.; ESTRADA, ERNESTO. Geometrical and spectral study of beta-skeleton graphs. Physical Review E, v. 100, n. 6 DEC 19 2019. Web of Science Citations: 0.

HERRERA-GONZALEZ, I. F.; MENDEZ-BERMUDEZ, J. A. Heat conduction in harmonic chains with Levy-type disorder. Physical Review E, v. 100, n. 5 NOV 8 2019. Web of Science Citations: 0.