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(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

Thermodynamic characterization of networks using graph polynomials

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Autor(es):
Ye, Cheng [1] ; Comin, Cesar H. [2] ; Peron, Thomas K. D. M. [2] ; Silva, Filipi N. [2] ; Rodrigues, Francisco A. [3] ; Costa, Luciano da F. [2] ; Torsello, Andrea [4] ; Hancock, Edwin R. [1]
Número total de Autores: 8
Afiliação do(s) autor(es):
[1] Univ York, Dept Comp Sci, York YO10 5GH, N Yorkshire - England
[2] Univ Sao Paulo, Inst Phys Sao Carlos, BR-13560970 Sao Paulo - Brazil
[3] Univ Sao Paulo, Inst Math & Comp Sci, BR-13560970 Sao Paulo - Brazil
[4] Ca Foscari Univ Venice, Dept Environm Sci Informat & Stat, I-30123 Venice - Italy
Número total de Afiliações: 4
Tipo de documento: Artigo Científico
Fonte: Physical Review E; v. 92, n. 3 SEP 25 2015.
Citações Web of Science: 10
Resumo

In this paper, we present a method for characterizing the evolution of time-varying complex networks by adopting a thermodynamic representation of network structure computed from a polynomial (or algebraic) characterization of graph structure. Commencing from a representation of graph structure based on a characteristic polynomial computed from the normalized Laplacian matrix, we show how the polynomial is linked to the Boltzmann partition function of a network. This allows us to compute a number of thermodynamic quantities for the network, including the average energy and entropy. Assuming that the system does not change volume, we can also compute the temperature, defined as the rate of change of entropy with energy. All three thermodynamic variables can be approximated using low-order Taylor series that can be computed using the traces of powers of the Laplacian matrix, avoiding explicit computation of the normalized Laplacian spectrum. These polynomial approximations allow a smoothed representation of the evolution of networks to be constructed in the thermodynamic space spanned by entropy, energy, and temperature. We show how these thermodynamic variables can be computed in terms of simple network characteristics, e.g., the total number of nodes and node degree statistics for nodes connected by edges. We apply the resulting thermodynamic characterization to real-world time-varying networks representing complex systems in the financial and biological domains. The study demonstrates that the method provides an efficient tool for detecting abrupt changes and characterizing different stages in network evolution. (AU)

Processo FAPESP: 13/26416-9 - Modelagem de processos dinâmicos em redes complexas
Beneficiário:Francisco Aparecido Rodrigues
Linha de fomento: Auxílio à Pesquisa - Regular
Processo FAPESP: 12/50986-7 - Graph spectra and complex network evolution
Beneficiário:Luciano da Fontoura Costa
Linha de fomento: Auxílio à Pesquisa - Regular
Processo FAPESP: 11/22639-8 - Estudo da relação estrutura-dinâmica em redes modulares
Beneficiário:Cesar Henrique Comin
Linha de fomento: Bolsas no Brasil - Doutorado
Processo FAPESP: 12/22160-7 - Sincronização de osciladores de Kuramoto em redes complexas
Beneficiário:Thomas Kaue Dal Maso Peron
Linha de fomento: Bolsas no Brasil - Doutorado
Processo FAPESP: 11/50761-2 - Modelos e métodos de e-Science para ciências da vida e agrárias
Beneficiário:Roberto Marcondes Cesar Junior
Linha de fomento: Auxílio à Pesquisa - Temático