Julho 2025 vol. 11 num. 1 - XV Encontro Científico de Física Aplicada

Artigo - Open Access.

Idioma principal | Segundo idioma

Mecânica Estatística e Redes Complexas

Statistical Mechanics and Networks Complexities

Santos, Tarcis Alvan oliva dos ; HOFFMANN, ELISANGELA ;

Artigo:

Este estudo investigou a articulação dos fundamentos da mecânica estatística ao estudo de redes complexas, por meio de uma revisão de literatura sistematizada na base de dados Scopus. A pesquisa foi conduzida em duas etapas: uma análise bibliométrica de 252 artigos e, posteriormente, uma leitura integral dos 10% mais citados (26 artigos) construtores de campo. Os resultados revelaram a centralidade de modelos teóricos como os de Albert e Barabási (2002) e Dorogovtsev e Mendes (2002), que consolidaram a transição da teoria dos grafos para modelos dinâmicos baseados em princípios estatísticos. Os documentos analisados foram agrupados em três categorias: (1) consolidação teórica, com ênfase nos fundamentos conceituais; (2) expansão metodológica e interdisciplinar, com destaque para inovações computacionais e métricas aplicadas; e (3) relevância empírica, a partir da aplicação de modelos em sistemas reais como redes elétricas, financeiras e sociais. O estudo aponta que a mecânica estatística oferece um arcabouço robusto para o entendimento de propriedades emergentes em redes complexas, especialmente em contextos dinâmicos.

Artigo:

This study investigated the articulation of the foundations of statistical mechanics with the study of complex networks, through a systematized literature review in the Scopus database. The research was conducted in two stages: a
bibliometric analysis of 252 articles and, subsequently, a full reading of the top 10% most cited (26 articles) considered field-building. The results revealed the centrality of theoretical models such as those of Albert and Barabási (2002) and Dorogovtsev and Mendes (2002), which established the transition from graph theory to dynamic models based on statistical principles. The analyzed documents were grouped into three categories: (1) theoretical consolidation, with emphasis on conceptual foundations; (2) methodological and interdisciplinary expansion, highlighting computational innovations and applied metrics; and (3) empirical relevance, through the application of models in real systems such as electrical, financial, and social networks. The study indicates that statistical mechanics provides a solid framework for understanding emergent properties in complex networks, especially in dynamic contexts.

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Palavras-chave: Redes Complexas, Mecânica Estatística, Climatologia,

Palavras-chave: Complex Networks, Statistical Mechanics, Climatology,

DOI: 10.5151/xvecfa-2025021

Referências bibliográficas
  • [1] ALBERT, R.; BARABÁSI, A-L. Statistical mechanics of complex networks. *Reviews of Modern Physics*, v. 74, n. 1, p. 47-97, 2002. [https://doi.org/10.1103/RevModPhys.74.47](https://doi.org/10.1103/RevModPhys.74.47)
  • [2] DOROGOVTSEV, S. N.; MENDES, J. F. F. *Evolution of Networks: From Biological Nets to the Internet and WWW*. Oxford University Press, 2003. [https://doi.org/10.1093/acprof\:oso/9780198515906.001.0001](https://doi.org/10.1093/acprof:oso/9780198515906.001.0001)
  • [3] ERDŐS, P.; RÉNYI, A. On the evolution of random graphs. *Publication of the Mathematical Institute of the Hungarian Academy of Sciences*, v. 5, p. 17-60, 1959. [https://static.actevity.hu/\~p\_erdos/1960.pdf](https://static.actevity.hu/~p_erdos/1960.pdf)
  • [4] BORNMMAN, L. Do altmetrics point to the broader impact of research? An overview of benefits and disadvantages of altmetrics. *Journal of informetrics*, v. 8, n. 4, p. 895-903, 201 [https://doi.org/10.1016/j.joi.20109.005](https://doi.org/10.1016/j.joi.20109.005)
  • [5] KRIKOUV, D.; PAPADOPOULOS, F.; KITSÁK, M.; VAHDAT, A.; BOGUÑA, M. Hyperbolic geometry of complex networks. *Physical Review E—Statistical, Nonlinear, and Soft Matter Physics*, v. 82, n. 3, p. 036106, 2010. [https://doi.org/10.1103/PhysRevE.82.036106](https://doi.org/10.1103/PhysRevE.82.036106)
  • [6] SORRENTINO, F.; DI BERNARDO, M.; GAROFALO, F.; CHEN, G. Controllability of complex networks via pinning. *Physical Review E—Statistical, Nonlinear, and Soft Matter Physics*, v. 75, n. 4, p. 046103, 2007. [https://doi.org/10.1103/PhysRevE.75.046103](https://doi.org/10.1103/PhysRevE.75.046103)
  • [7] BRAHA, D.; BAR-YAM, Y. The statistical mechanics of complex product development: Empirical and analytical results. *Management Science*, v. 53, n. 7, p. 1127-1145, 200 [https://doi.org/10.1287/mnsc.1060.0672](https://doi.org/10.1287/mnsc.1060.0672)
  • [8] TOVONEN, R.; ONNELA, J. P.; SARAMÄKI, J.; HYVONEN, J.; KASKI, K. A model for social networks. *Physica A: Statistical Mechanics and Its Applications*, v. 371, n. 2, p. 851-860, 2006. [https://doi.org/10.1016/j.physa.2006.03.050](https://doi.org/10.1016/j.physa.2006.03.050)
  • [9] GUILLAUME, J. L.; LATAPY, M. Bipartite structure of all complex networks. *Information Processing Letters*, v. 90, n. 5, p. 215-221, 2004. [https://hal.science/hal-00016855/document](https://hal.science/hal-00016855/document)
  • [10] GUILLAUME, J. L.; LATAPY, M. Bipartite graphs as models of complex networks. In: *Workshop on Combinatorial and Algorithmic Aspects of Networking*, p. 127-139. [https://gephi.org/users/publications/2004-guillaume-latapy-bipartite.pdf](https://gephi.org/users/publications/2004-guillaume-latapy-bipartite.pdf)
  • [11] GUMERA MANRIQUE, R.; ARENAS, A.; DIAZ GUILERA, A.; GIRALT, F. Dynamical properties of model communication networks. *Physical Review E*, v. 66, n. 2, p. 026704, 2002. [https://doi.org/10.1103/PhysRevE.66.026704](https://doi.org/10.1103/PhysRevE.66.026704)
  • [12] ESTRADA, E.; HATANO, N. Statistical-mechanical approach to subgraph centrality in complex networks. *Chemical Physics Letters*, v. 439, n. 1-3, p. 247-251, 2007. [https://doi.org/10.1016/j.cplett.2007.03.089](https://doi.org/10.1016/j.cplett.2007.03.089)
  • [13] SÁNCHEZ, A. D.; LÓPEZ, J. M.; RODRIGUEZ, M. A. Nonequilibrium phase transitions in directed small-world networks. *Physical Review Letters*, v. 88, n. 4, p. 048701, 2002. [https://doi.org/10.1103/PhysRevLett.88.048701](https://doi.org/10.1103/PhysRevLett.88.048701)
  • [14] AO, P. Potential in noise driven differential equations: novel construction. *Journal of Physics A: Mathematical and General*, v. 37, n. 3, p. L25, 2004. [https://doi.org/10.1088/0305-4470/37/3/L01](https://doi.org/10.1088/0305-4470/37/3/L01)
  • [15] ROZENFELD, H. D.; SONG, C.; MAKSE, H. A. Small-world to fractal transition in complex networks: a renormalization group approach. *Physical Review Letters*, v. 104, n. 2, p. 025701, 2010. [https://doi.org/10.1103/PhysRevLett.104.025701](https://doi.org/10.1103/PhysRevLett.104.025701)
  • [16] CALLASTRA, L.; BARRAT, A.; BARTHÉLEMY, M.; VESPIGNANI, A. Vulnerability of weighted networks. *Journal of Statistical Mechanics: Theory and Experiment*, v. 2006, n. 04, P04006, 2006. [https://doi.org/10.1088/1742-5468/2006/04/P04006](https://doi.org/10.1088/1742-5468/2006/04/P04006)
  • [17] HOLME, P.; SARAMÄKI, J. Temporal networks. *Physics Reports*, v. 519, n. 3, p. 97-125, 2012. [https://doi.org/10.1016/j.physrep.2012.03.001](https://doi.org/10.1016/j.physrep.2012.03.001)
  • [18] DE DOMENICO, M. Multilayer modeling of complex networks. *Nature Reviews Physics*, v. 5, p. 340-321, 2023. [https://doi.org/10.48550/arXiv.1604.02021](https://doi.org/10.48550/arXiv.1604.02021)
Como citar:

Santos, Tarcis Alvan oliva dos; HOFFMANN, ELISANGELA; "Mecânica Estatística e Redes Complexas", p. 116-123 . In: Anais do XV Encontro Científico de Física Aplicada. São Paulo: Blucher, 2025.
ISSN 2358-2359, DOI 10.5151/xvecfa-2025021

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