IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v404y2014icp341-358.html
   My bibliography  Save this article

Correlation of automorphism group size and topological properties with program-size complexity evaluations of graphs and complex networks

Author

Listed:
  • Zenil, Hector
  • Soler-Toscano, Fernando
  • Dingle, Kamaludin
  • Louis, Ard A.

Abstract

We show that numerical approximations of Kolmogorov complexity (K) of graphs and networks capture some group-theoretic and topological properties of empirical networks, ranging from metabolic to social networks, and of small synthetic networks that we have produced. That K and the size of the group of automorphisms of a graph are correlated opens up interesting connections to problems in computational geometry, and thus connects several measures and concepts from complexity science. We derive these results via two different Kolmogorov complexity approximation methods applied to the adjacency matrices of the graphs and networks. The methods used are the traditional lossless compression approach to Kolmogorov complexity, and a normalised version of a Block Decomposition Method (BDM) based on algorithmic probability theory.

Suggested Citation

  • Zenil, Hector & Soler-Toscano, Fernando & Dingle, Kamaludin & Louis, Ard A., 2014. "Correlation of automorphism group size and topological properties with program-size complexity evaluations of graphs and complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 404(C), pages 341-358.
    • Handle: RePEc:eee:phsmap:v:404:y:2014:i:c:p:341-358
    DOI: 10.1016/j.physa.2014.02.060
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437114001691
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2014.02.060?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kim, Jongkwang & Wilhelm, Thomas, 2008. "What is a complex graph?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(11), pages 2637-2652.
    2. Matthias Dehmer & Lavanya Sivakumar, 2012. "Recent Developments in Quantitative Graph Theory: Information Inequalities for Networks," PLOS ONE, Public Library of Science, vol. 7(2), pages 1-13, February.
    3. Jean-Paul Delahaye & Hector Zenil, 2012. "Numerical Evaluation of Algorithmic Complexity for Short Strings: A Glance into the Innermost Structure of Randomness," Post-Print hal-00825530, HAL.
    4. H. Jeong & B. Tombor & R. Albert & Z. N. Oltvai & A.-L. Barabási, 2000. "The large-scale organization of metabolic networks," Nature, Nature, vol. 407(6804), pages 651-654, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Fernando Soler-Toscano & Hector Zenil & Jean-Paul Delahaye & Nicolas Gauvrit, 2014. "Calculating Kolmogorov Complexity from the Output Frequency Distributions of Small Turing Machines," PLOS ONE, Public Library of Science, vol. 9(5), pages 1-18, May.
    2. Fernando Soler-Toscano & Hector Zenil, 2017. "A Computable Measure of Algorithmic Probability by Finite Approximations with an Application to Integer Sequences," Complexity, Hindawi, vol. 2017, pages 1-10, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lavanya Sivakumar & Matthias Dehmer, 2012. "Towards Information Inequalities for Generalized Graph Entropies," PLOS ONE, Public Library of Science, vol. 7(6), pages 1-14, June.
    2. Frank Emmert-Streib, 2013. "Structural Properties and Complexity of a New Network Class: Collatz Step Graphs," PLOS ONE, Public Library of Science, vol. 8(2), pages 1-14, February.
    3. Mikołaj Morzy & Tomasz Kajdanowicz & Przemysław Kazienko, 2017. "On Measuring the Complexity of Networks: Kolmogorov Complexity versus Entropy," Complexity, Hindawi, vol. 2017, pages 1-12, November.
    4. Jin Wang & Bo Huang & Xuefeng Xia & Zhirong Sun, 2006. "Funneled Landscape Leads to Robustness of Cell Networks: Yeast Cell Cycle," PLOS Computational Biology, Public Library of Science, vol. 2(11), pages 1-10, November.
    5. Jorge Peña & Yannick Rochat, 2012. "Bipartite Graphs as Models of Population Structures in Evolutionary Multiplayer Games," PLOS ONE, Public Library of Science, vol. 7(9), pages 1-13, September.
    6. Dingle, Kamaludin & Kamal, Rafiq & Hamzi, Boumediene, 2023. "A note on a priori forecasting and simplicity bias in time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    7. Tamás Nepusz & Tamás Vicsek, 2013. "Hierarchical Self-Organization of Non-Cooperating Individuals," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-9, December.
    8. Aslam, Faheem & Aziz, Saqib & Nguyen, Duc Khuong & Mughal, Khurrum S. & Khan, Maaz, 2020. "On the efficiency of foreign exchange markets in times of the COVID-19 pandemic," Technological Forecasting and Social Change, Elsevier, vol. 161(C).
    9. Jiang, Jingchi & Zheng, Jichuan & Zhao, Chao & Su, Jia & Guan, Yi & Yu, Qiubin, 2016. "Clinical-decision support based on medical literature: A complex network approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 459(C), pages 42-54.
    10. Gerhardt, Günther J.L. & Lemke, Ney & Corso, Gilberto, 2006. "Network clustering coefficient approach to DNA sequence analysis," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 1037-1045.
    11. Laurienti, Paul J. & Joyce, Karen E. & Telesford, Qawi K. & Burdette, Jonathan H. & Hayasaka, Satoru, 2011. "Universal fractal scaling of self-organized networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3608-3613.
    12. Chen, Qinghua & Shi, Dinghua, 2004. "The modeling of scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 240-248.
    13. Liu, X. & Murata, T., 2010. "Advanced modularity-specialized label propagation algorithm for detecting communities in networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(7), pages 1493-1500.
    14. Wen, Xiangxi & Tu, Congliang & Wu, Minggong, 2018. "Node importance evaluation in aviation network based on “No Return” node deletion method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 546-559.
    15. Lawford, Steve & Mehmeti, Yll, 2020. "Cliques and a new measure of clustering: With application to U.S. domestic airlines," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    16. J. J. Esquivel-Gómez & J. G. Barajas-Ramírez, 2024. "Rapid disease spread on dense networks with power-law topology," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(5), pages 1-10, May.
    17. Wang, Huan & Xu, Chuan-Yun & Hu, Jing-Bo & Cao, Ke-Fei, 2014. "A complex network analysis of hypertension-related genes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 166-176.
    18. Selen Onel & Abe Zeid & Sagar Kamarthi, 2011. "The structure and analysis of nanotechnology co-author and citation networks," Scientometrics, Springer;Akadémiai Kiadó, vol. 89(1), pages 119-138, October.
    19. Chung-Yen Yu & Yung-Ting Chuang & Hsi-Peng Kuan, 2017. "Understanding Faculty Collaboration and Productivity: A Case Study," Asian Social Science, Canadian Center of Science and Education, vol. 13(3), pages 1-1, March.
    20. Ashty S. Karim & Dylan M. Brown & Chloé M. Archuleta & Sharisse Grannan & Ludmilla Aristilde & Yogesh Goyal & Josh N. Leonard & Niall M. Mangan & Arthur Prindle & Gabriel J. Rocklin & Keith J. Tyo & L, 2024. "Deconstructing synthetic biology across scales: a conceptual approach for training synthetic biologists," Nature Communications, Nature, vol. 15(1), pages 1-14, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:404:y:2014:i:c:p:341-358. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.