IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v389y2010i23p5521-5529.html
   My bibliography  Save this article

Motif structure and cooperation in real-world complex networks

Author

Listed:
  • Salehi, Mostafa
  • Rabiee, Hamid R.
  • Jalili, Mahdi

Abstract

Networks of dynamical nodes serve as generic models for real-world systems in many branches of science ranging from mathematics to physics, technology, sociology and biology. Collective behavior of agents interacting over complex networks is important in many applications. The cooperation between selfish individuals is one of the most interesting collective phenomena. In this paper we address the interplay between the motifs’ cooperation properties and their abundance in a number of real-world networks including yeast protein–protein interaction, human brain, protein structure, email communication, dolphins’ social interaction, Zachary karate club and Net-science coauthorship networks. First, the amount of cooperativity for all possible undirected subgraphs with three to six nodes is calculated. To this end, the evolutionary dynamics of the Prisoner’s Dilemma game is considered and the cooperativity of each subgraph is calculated as the percentage of cooperating agents at the end of the simulation time. Then, the three- to six-node motifs are extracted for each network. The significance of the abundance of a motif, represented by a Z-value, is obtained by comparing them with some properly randomized versions of the original network. We found that there is always a group of motifs showing a significant inverse correlation between their cooperativity amount and Z-value, i.e. the more the Z-value the less the amount of cooperativity. This suggests that networks composed of well-structured units do not have good cooperativity properties.

Suggested Citation

  • Salehi, Mostafa & Rabiee, Hamid R. & Jalili, Mahdi, 2010. "Motif structure and cooperation in real-world complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(23), pages 5521-5529.
  • Handle: RePEc:eee:phsmap:v:389:y:2010:i:23:p:5521-5529
    DOI: 10.1016/j.physa.2010.08.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437110006746
    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.2010.08.001?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. repec:cup:cbooks:9780511771576 is not listed on IDEAS
    2. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    3. Hisashi Ohtsuki & Christoph Hauert & Erez Lieberman & Martin A. Nowak, 2006. "A simple rule for the evolution of cooperation on graphs and social networks," Nature, Nature, vol. 441(7092), pages 502-505, May.
    4. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, April.
    5. Luthi, Leslie & Pestelacci, Enea & Tomassini, Marco, 2008. "Cooperation and community structure in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(4), pages 955-966.
    6. Ding, Fei & Liu, Yun & Shen, Bo & Si, Xia-Meng, 2010. "An evolutionary game theory model of binary opinion formation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(8), pages 1745-1752.
    7. Christoph Hauert & Michael Doebeli, 2004. "Spatial structure often inhibits the evolution of cooperation in the snowdrift game," Nature, Nature, vol. 428(6983), pages 643-646, April.
    8. Huang, Chung-Yuan & Sun, Chuen-Tsai & Cheng, Chia-Ying & Hsieh, Ji-Lung, 2007. "Bridge and brick motifs in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 340-350.
    9. Moreno Vega, Yamir & Vázquez-Prada, Miguel & F. Pacheco, Amalio, 2004. "Fitness for synchronization of network motifs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 279-287.
    10. Easley,David & Kleinberg,Jon, 2010. "Networks, Crowds, and Markets," Cambridge Books, Cambridge University Press, number 9780521195331, 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. Shen, Yi, 2014. "The similarity of weights on edges and discovering of community structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 560-570.
    2. Zhou Wen & Chen Wei & Wang Zhanzhao & Ma Yonghong, 2015. "Generating Behavior in the University-Industry Collaboration Network: Based on the Configuration of Motifs," Journal of Systems Science and Information, De Gruyter, vol. 3(5), pages 434-450, October.

    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. Michael Foley & Rory Smead & Patrick Forber & Christoph Riedl, 2021. "Avoiding the bullies: The resilience of cooperation among unequals," PLOS Computational Biology, Public Library of Science, vol. 17(4), pages 1-18, April.
    2. Huang, Keke & Zheng, Xiaoping & Su, Yunpeng, 2015. "Effect of heterogeneous sub-populations on the evolution of cooperation," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 681-687.
    3. Chunyan Zhang & Jianlei Zhang & Guangming Xie & Long Wang & Matjaž Perc, 2011. "Evolution of Interactions and Cooperation in the Spatial Prisoner's Dilemma Game," PLOS ONE, Public Library of Science, vol. 6(10), pages 1-7, October.
    4. Li, Yan & Ye, Hang, 2018. "Effect of the migration mechanism based on risk preference on the evolution of cooperation," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 621-632.
    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. Zhao, Zhengwu & Zhang, Chunyan, 2023. "The mechanisms of labor division from the perspective of task urgency and game theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    7. Takahiro Ezaki & Naoki Masuda, 2017. "Reinforcement learning account of network reciprocity," PLOS ONE, Public Library of Science, vol. 12(12), pages 1-8, December.
    8. Rong-Hua Li & Jeffrey Xu Yu & Jiyuan Lin, 2013. "Evolution of Cooperation in Spatial Traveler's Dilemma Game," PLOS ONE, Public Library of Science, vol. 8(3), pages 1-11, March.
    9. Han, Jia-Xu & Wang, Rui-Wu, 2023. "Complex interactions promote the frequency of cooperation in snowdrift game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    10. Wang, Zhen & Chen, Tong & Wang, Yongjie, 2017. "Leadership by example promotes the emergence of cooperation in public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 100-105.
    11. Qiguang An & Hongfeng Guo & Yating Zheng, 2022. "On Robust Stability and Stabilization of Networked Evolutionary Games with Time Delays," Mathematics, MDPI, vol. 10(15), pages 1-12, July.
    12. Sabin Lessard, 2011. "Effective Game Matrix and Inclusive Payoff in Group-Structured Populations," Dynamic Games and Applications, Springer, vol. 1(2), pages 301-318, June.
    13. Silveira, Douglas & Vasconcelos, Silvinha, 2020. "Essays on duopoly competition with asymmetric firms: Is profit maximization always an evolutionary stable strategy?," International Journal of Production Economics, Elsevier, vol. 225(C).
    14. Alberto Antonioni & Maria Paula Cacault & Rafael Lalive & Marco Tomassini, 2013. "Coordination on Networks: Does Topology Matter?," PLOS ONE, Public Library of Science, vol. 8(2), pages 1-11, February.
    15. Lefeng Cheng & Pan Peng & Wentian Lu & Pengrong Huang & Yang Chen, 2024. "Study of Flexibility Transformation in Thermal Power Enterprises under Multi-Factor Drivers: Application of Complex-Network Evolutionary Game Theory," Mathematics, MDPI, vol. 12(16), pages 1-23, August.
    16. Mullon, Charles & Peña, Jorge & Lehmann, Laurent, 2023. "Evolution of environmentally mediated social interactions under isolation by distance," TSE Working Papers 23-1476, Toulouse School of Economics (TSE).
    17. Spiekermann, Kai, 2009. "Sort out your neighbourhood: public good games on dynamic networks," LSE Research Online Documents on Economics 26739, London School of Economics and Political Science, LSE Library.
    18. Fabio Della Rossa & Fabio Dercole & Anna Di Meglio, 2020. "Direct Reciprocity and Model-Predictive Strategy Update Explain the Network Reciprocity Observed in Socioeconomic Networks," Games, MDPI, vol. 11(1), pages 1-28, March.
    19. Sarkar, Bijan, 2021. "The cooperation–defection evolution on social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 584(C).
    20. Li, Bin-Quan & Wu, Zhi-Xi & Guan, Jian-Yue, 2022. "Critical thresholds of benefit distribution in an extended snowdrift game model," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

    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:389:y:2010:i:23:p:5521-5529. 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.