Skip to main content
SpringerLink
Log in

Shannon Entropy in Time–Varying Clique Networks

  • Conference paper
  • First Online:
Complex Networks and Their Applications VIII (COMPLEX NETWORKS 2019)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 881))

Included in the following conference series:

  • 3127 Accesses

Abstract

Recent works have used information theory in complex networks. Studies often discuss entropy in the degree distributions of a network. However, there is no specific work for entropy in clique networks. In this regard, this work proposes a method to calculate clique network entropy, as well as its theoretical maximum and minimum values. The entropies are calculated for the dataset of the semantic networks of titles of scientific papers from the journals Nature and Science for approximately a decade. Journals are modeled as time–varying graphs and each system is analyzed from a time sliding window. The results show the entropy values of vertices and edges in each window arranged in time series, and also suggest the moment which has more or less vocabulary diversification when this diversity turns the studied journals closer or move them away. For that matter, this report contributes to the studies on clique networks and the diffusion of human knowledge in journals of high scientific impact.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    For Nature \( T = 514 \,\text{weeks} \) and for Science \( T = 512\, \text{weeks} \).

  2. 2.

    Depending on the investigated system, it may not be necessary to use all of these conditions or to include or replace the existing one.

References

  1. Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27(3), 379–423 (1948)

    Article  MathSciNet  Google Scholar 

  2. Mousavian, Z., Kavousi, K., Masoudi–Nejad, A.: Information theory in systems biology. Part I: gene regulatory and metabolic networks. In: Seminars in Cell & Developmental Biology, vol. 51, pp. 3–13. Academic Press (2016)

    Google Scholar 

  3. Mishra, S., Ayyub, B.M.: Shannon entropy for quantifying uncertainty and risk in economic disparity. Risk Anal. 39(10), 2160–2181 (2019)

    Article  Google Scholar 

  4. Nascimento, W.S., Prudente, F.V.: Shannon entropy: a study of confined hydrogenic–like atoms. Chem. Phys. Lett. 691, 401–407 (2018)

    Article  Google Scholar 

  5. Zenil, H., Kiani, N.A., Tegnér, J.: Methods of information theory and algorithmic complexity for network biology. In: Seminars in Cell & Developmental Biology, vol. 51, pp. 32–43. Academic Press (2016)

    Google Scholar 

  6. Zurek, W.H.: Complexity, vol. 8. Entropy and the Physics of Information. CRC Press, Boca Raton (2018)

    Google Scholar 

  7. Gao, X., Gallicchio, E., Roitberg, A.E.: The generalized Boltzmann distribution is the only distribution in which the Gibbs-Shannon entropy equals the thermodynamic entropy. J. Chem. Phys. 151(3), 034113 (2019)

    Article  Google Scholar 

  8. Solé, R.V., Valverde, S.: Information theory of complex networks: on evolution and architectural constraints. In: Complex Networks, pp. 189–207. Springer, Berlin (2004)

    Chapter  Google Scholar 

  9. Ji, L., Bing–Hong, W., Wen–Xu, W., Tao, Z.: Network entropy based on topology configuration and its computation to random networks. Chin. Phys. Lett. 25(11), 4177 (2008)

    Article  Google Scholar 

  10. Viol, A., Palhano-Fontes, F., Onias, H., de Araujo, D.B., Hövel, P., Viswanathan, G.M.: Characterizing complex networks using entropy–degree diagrams: unveiling changes in functional brain connectivity induced by Ayahuasca. Entropy 21(2), 128 (2019)

    Article  MathSciNet  Google Scholar 

  11. Nicosia, V., Tang, J., Musolesi, M., Russo, G., Mascolo, C., Latora, V.: Components in time varying–graphs. Chaos: Interdisc. J. Nonlinear Sci. 22(2), 023101 (2012)

    Article  MathSciNet  Google Scholar 

  12. Casteigts, A., Flocchini, P., Quattrociocchi, W., Santoro, N.: Time–varying graphs and dynamic networks. Int. J. Parallel Emergent Distrib. Syst. 27(5), 387–408 (2012)

    Article  Google Scholar 

  13. Holme, P., Saramäki, J.: Temporal networks. Phys. Rep. 519(3), 97–125 (2012)

    Article  Google Scholar 

  14. Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)

    Article  MathSciNet  Google Scholar 

  15. Newman, M.E.: Scientific collaboration networks. I. Network construction and fundamental results. Phys. Rev. E 64(1), 016131 (2001)

    Article  MathSciNet  Google Scholar 

  16. Caldeira, S.M., Lobao, T.P., Andrade, R.F.S., Neme, A., Miranda, J.V.: The network of concepts in written texts. Eur. Phys. J. B-Condens. Matter Complex Syst. 49(4), 523–529 (2006)

    Article  Google Scholar 

  17. Teixeira, G.M., Aguiar, M.S.F., Carvalho, C.F., Dantas, D.R., Cunha, M.V., Morais, J.H.M., Pereira, H.B.B., Miranda, J.G.V.: Complex semantic networks. Int. J. Modern Phys. C 21(03), 333–347 (2010)

    Article  Google Scholar 

  18. Pereira, H.D.B., Fadigas, I.S., Senna, V., Moret, M.A.: Semantic networks based on titles of scientific papers. Phys. A: Stat. Mech. Appl. 390(6), 1192–1197 (2011)

    Article  Google Scholar 

  19. Pereira, H.B.B., Fadigas, I.S., Monteiro, R.L.S., Cordeiro, A.J.A., Moret, M.A.: Density: a measure of the diversity of concepts addressed in semantic networks. Phys. A: Stat. Mech. Appl. 441, 81–84 (2016)

    Article  Google Scholar 

  20. Grilo, M., Fadigas, I.S., Miranda, J.G.V., Cunha, M.V., Monteiro, R.L.S., Pereira, H.B.B.: Robustness in semantic networks based on cliques. Phys. A: Stat. Mech. Appl. 472, 94–102 (2017)

    Article  Google Scholar 

  21. Brillouin, L.: Science and Information Theory. Courier Corporation, Chelmsford (2013)

    MATH  Google Scholar 

  22. Fadigas, I.D.S., Pereira, H.B.D.B.: A network approach based on cliques. Phys. A: Stat. Mech. Appl. 392(10), 2576–2587 (2013)

    Article  Google Scholar 

  23. Adamcsek, B., Palla, G., Farkas, I.J., Derényi, I., Vicsek, T.: CFinder: locating cliques and overlapping modules in biological networks. Bioinformatics 22(8), 1021–1023 (2006)

    Article  Google Scholar 

  24. Derényi, I., Palla, G., Vicsek, T.: Clique percolation in random networks. Phys. Rev. Lett. 94(16), 160202 (2005)

    Article  Google Scholar 

  25. Lima–Neto, J.L.A., Cunha, M., Pereira, H.B.B.: Redes semânticas de discursos orais de membros de grupos de ajuda mútua. Obra Digit.: J. Commun. Technol. 14, 51–66 (2018)

    Article  Google Scholar 

  26. Henrique, T., de Sousa Fadigas, I., Rosa, M.G., de Barros Pereira, H.B.: Mathematics education semantic networks. Soc. Netw. Anal. Mining 4(1), 200 (2014)

    Article  Google Scholar 

  27. Cunha, M.V., Rosa, M.G., Fadigas, I.S., Miranda, J.G.V., Pereira, H.B.B.: Redes de títulos de artigos científicos variáveis no tempo. In: Anais do II Brazilian Workshop on Social Network Analysis and Mining, CSBC 2013, Maceió–AL, pp. 194–205 (2013)

    Google Scholar 

  28. Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature 393(4), 440–442 (1998)

    Article  Google Scholar 

Download references

Acknowledgment

This paper is being financially supported by the Rectory of Research and Innovation of the Federal Institute of Bahia (PRPGI-IFBA) and the Senai Cimatec-BA University Center, from its preparation to its presentation at Complex Networks 2019.

Author information

Authors and Affiliations

  1. Centro Universitário SENAI CIMATEC, Salvador, BA, 41650-010, Brazil

    Marcelo do Vale Cunha, Carlos César Ribeiro Santos, Marcelo Albano Moret & Hernane Borges de Barros Pereira

  2. Instituto Federal da Bahia, Barreiras, BA, 47808-006, Brazil

    Marcelo do Vale Cunha

  3. Universidade do Estado da Bahia, Salvador, BA, 41150-000, Brazil

    Marcelo Albano Moret & Hernane Borges de Barros Pereira

Authors
  1. Marcelo do Vale Cunha
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Carlos César Ribeiro Santos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marcelo Albano Moret
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hernane Borges de Barros Pereira
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marcelo do Vale Cunha .

Editor information

Editors and Affiliations

  1. University of Burgundy, Dijon Cedex, France

    Hocine Cherifi

  2. Università degli Studi di Milano, Milan, Italy

    Sabrina Gaito

  3. University of Aveiro, Aveiro, Portugal

    José Fernendo Mendes

  4. Universidad Carlos III de Madrid, Leganés, Madrid, Spain

    Esteban Moro

  5. Indiana University, Bloomington, IN, USA

    Luis Mateus Rocha

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

do Vale Cunha, M., Santos, C.C.R., Moret, M.A., Pereira, H.B.d.B. (2020). Shannon Entropy in Time–Varying Clique Networks. In: Cherifi, H., Gaito, S., Mendes, J., Moro, E., Rocha, L. (eds) Complex Networks and Their Applications VIII. COMPLEX NETWORKS 2019. Studies in Computational Intelligence, vol 881. Springer, Cham. https://doi.org/10.1007/978-3-030-36687-2_42

Download citation

Publish with us

Policies and ethics

Search

Navigation