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Role models for complex networks

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  • J. Reichardt
  • D. R. White

Abstract

We present a framework for automatically decomposing (“block-modeling”) the functional classes of agents within a complex network. These classes are represented by the nodes of an image graph (“block model”) depicting the main patterns of connectivity and thus functional roles in the network. Using a first principles approach, we derive a measure for the fit of a network to any given image graph allowing objective hypothesis testing. From the properties of an optimal fit, we derive how to find the best fitting image graph directly from the network and present a criterion to avoid overfitting. The method can handle both two-mode and one-mode data, directed and undirected as well as weighted networks and allows for different types of links to be dealt with simultaneously. It is non-parametric and computationally efficient. The concepts of structural equivalence and modularity are found as special cases of our approach. We apply our method to the world trade network and analyze the roles individual countries play in the global economy. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Suggested Citation

  • J. Reichardt & D. R. White, 2007. "Role models for complex networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 60(2), pages 217-224, November.
    • Handle: RePEc:spr:eurphb:v:60:y:2007:i:2:p:217-224
    DOI: 10.1140/epjb/e2007-00340-y
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    Citations

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    Cited by:

    1. Roland Lantner & Didier Lebert, 2013. "Dominance, dependence and interdependence in linear structures. A theoretical model and an application to the international trade flows," Post-Print halshs-00825477, HAL.
    2. Zhu, Zhen & Morrison, Greg & Puliga, Michelangelo & Chessa, Alessandro & Riccaboni, Massimo, 2018. "The similarity of global value chains: A network-based measure," Network Science, Cambridge University Press, vol. 6(4), pages 607-632, December.
    3. Cosma Rohilla Shalizi & Andrew C. Thomas, 2011. "Homophily and Contagion Are Generically Confounded in Observational Social Network Studies," Sociological Methods & Research, , vol. 40(2), pages 211-239, May.
    4. Roland Lantner & Didier Lebert, 2013. "Dominance, dependence and interdependence in linear structures. A theoretical model and an application to the international trade flows," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00825477, HAL.
    5. Lü, Linyuan & Zhou, Tao, 2011. "Link prediction in complex networks: A survey," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(6), pages 1150-1170.
    6. Frank Schweitzer & Giorgio Fagiolo & Didier Sornette & Fernando Vega-Redondo & Douglas R. White, 2009. "Economic Networks: What Do We Know And What Do We Need To Know?," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 12(04n05), pages 407-422.
    7. Giorgio Fagiolo, 2010. "The international-trade network: gravity equations and topological properties," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 5(1), pages 1-25, June.
    8. Blagus, Neli & Šubelj, Lovro & Weiss, Gregor & Bajec, Marko, 2015. "Sampling promotes community structure in social and information networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 432(C), pages 206-215.
    9. Barigozzi, Matteo & Fagiolo, Giorgio & Mangioni, Giuseppe, 2011. "Identifying the community structure of the international-trade multi-network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 2051-2066.
    10. Yi Yu & Jaeseung Baek & Ali Tosyali & Myong K. Jeong, 2024. "Robust asymmetric non-negative matrix factorization for clustering nodes in directed networks," Annals of Operations Research, Springer, vol. 341(1), pages 245-265, October.
    11. Stefan Pinkert & Jörg Schultz & Jörg Reichardt, 2010. "Protein Interaction Networks—More Than Mere Modules," PLOS Computational Biology, Public Library of Science, vol. 6(1), pages 1-13, January.
    12. Roland Lantner & Didier Lebert, 2013. "Dominance, dependence and interdependence in linear structures. A theoretical model and an application to the international trade flows," Documents de travail du Centre d'Economie de la Sorbonne 13043, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    13. Šubelj, Lovro & Bajec, Marko, 2014. "Group detection in complex networks: An algorithm and comparison of the state of the art," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 397(C), pages 144-156.
    14. Igor Mezić & Vladimir A. Fonoberov & Maria Fonoberova & Tuhin Sahai, 2019. "Spectral Complexity of Directed Graphs and Application to Structural Decomposition," Complexity, Hindawi, vol. 2019, pages 1-18, January.

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