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Dynamics on and of Complex Networks

DOOCN 2017: Dynamics On and Of Complex Networks III pp 83–111Cite as

Automatic Discovery of Families of Network Generative Processes

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Part of the book series: Springer Proceedings in Complexity ((SPCOM))

Abstract

Designing plausible network models typically requires scholars to form a priori intuitions on the key drivers of network formation. Oftentimes, these intuitions are supported by the statistical estimation of a selection of network evolution processes which will form the basis of the model to be developed. Machine learning techniques have lately been introduced to assist the automatic discovery of generative models. These approaches may more broadly be described as “symbolic regression,” where fundamental network dynamic functions, rather than just parameters, are evolved through genetic programming. This chapter first aims at reviewing the principles, efforts, and the emerging literature in this direction, which is very much aligned with the idea of creating artificial scientists. Our contribution then aims more specifically at building upon an approach recently developed by us (Menezes and Roth, Sci Rep 4:6284, 2014) in order to demonstrate the existence of families of networks that may be described by similar generative processes. In other words, symbolic regression may be used to group networks according to their inferred genotype (in terms of generative processes) rather than their observed phenotype (in terms of statistical/topological features). Our empirical case is based on an original dataset of 238 anonymized ego-centered networks of Facebook friends, further yielding insights on the formation of sociability networks.

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Notes

  1. 1.

    In terms of potential applications, this approach has been evoked in the context of human connectome modeling [3, 18], as an alternative to conventional social simulation models [7] or to appraise matrimonial preferences from genealogical networks [74].

  2. 2.

    To compute distances we use an heuristic based on a random walk, for (1) the exact computation is computationally intensive and, what is more, (2) new connections are also likely guided by a hop-by-hop navigation mechanism instead of an omniscient knowledge of the exact number of hops separating two given nodes.

  3. 3.

    ER is admittedly a basic null model. Yet, opting for a richer model is likely to induce bias: for instance, a fitness function based on a comparison with a configuration model would precisely incorporate target network degree distributions, making it impossible to directly approximate them.

  4. 4.

    We used the metric MDS manifold embedding provided by the scikit-learn Python module.

  5. 5.

    Given the undirected nature of these networks, we simplify the notation for generators that use only variables from either the origin side or target side. Suppose we have the generator 3⋅k i + d; here, this is equivalent to 3⋅k j + d, so we simply write 3⋅k + d.

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Acknowledgements

We are grateful to the members of our “Algopol” project team (ANR-12-CORD-0018) who organized most of the Facebook survey, including Irène Bastard, Dominique Cardon, Raphaël Charbey, Guilhem Fouetillou, Christophe Prieur, and Stéphane Raux. We further acknowledge interesting discussions with Jean-Philippe Cointet and David Fourquet regarding generative families, as well as the constructive feedback of our anonymous reviewers. This paper has been partially supported by the “Algodiv” grant (ANR-15-CE38-0001) funded by the ANR (French National Agency of Research).

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Authors and Affiliations

  1. Centre Marc Bloch (UMIFRE CNRS/MAE), Computational Social Science Team, Berlin, Germany

    Telmo Menezes & Camille Roth

  2. CNRS, Paris, France

    Camille Roth

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  1. Telmo Menezes
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Correspondence to Telmo Menezes .

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Editors and Affiliations

  1. Institute of Theoretical Physics, Technical University of Berlin, Berlin, Germany

    Fakhteh Ghanbarnejad

  2. Max Planck Institute for Informatics, Saarbrücken, Germany

    Rishiraj Saha Roy

  3. Department of Computational Social Science, GESIS, Leibniz Institute for the Social Science, Köln, Germany

    Fariba Karimi

  4. Université Catholique de Louvain, Louvain-la-Neuve, Belgium

    Jean-Charles Delvenne

  5. Department of Computer Science and Engineering, Indian Institute of Technology Kharagpur, Kharagpur, India

    Bivas Mitra

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Menezes, T., Roth, C. (2019). Automatic Discovery of Families of Network Generative Processes. In: Ghanbarnejad, F., Saha Roy, R., Karimi, F., Delvenne, JC., Mitra, B. (eds) Dynamics On and Of Complex Networks III. DOOCN 2017. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-030-14683-2_4

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