Abstract
The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree distribution. The degree distribution can either be theoretical or extracted from a real-world network. The main idea is to invert the recurrence equation commonly used to compute the degree distribution in order to find a convenient attachment function for node connections - commonly chosen as linear. We compute this attachment function for some classical distributions, as the power-law, broken power-law, geometric and Poisson distributions. We also use the model on an undirected version of the Twitter network, for which the degree distribution has an unusual shape.
This work has been supported by the French government through the UCA JEDI (ANR-15-IDEX-01) and EUR DS4H (ANR-17-EURE-004) Investments in the Future projects, by the SNIF project, and by Inria associated team EfDyNet.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Ahn, Y.-Y., Han, S., Kwak, H., Moon, S., Jeong, H.: Analysis of topological characteristics of huge online social networking services. In: Proceedings of the 16th International Conference on World Wide Web, pp. 835–844 (2007)
Albert, R., Barabási, A.-L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74(1), 47 (2002)
Bollobás, B.: A probabilistic proof of an asymptotic formula for the number of labelled regular graphs. Eur. J. Comb. 1(4), 311–316 (1980)
Bollobás, B., Borgs, C., Chayes, J.T., Riordan, O.: Directed scale-free graphs. In: SODA, vol. 3, pp. 132–139 (2003)
Broido, A.D., Clauset, A.: Scale-free networks are rare. Nat. Commun. 10(1), 1–10 (2019)
Cha, M., Mislove, A., Gummadi, K.P.: A measurement-driven analysis of information propagation in the Flickr social network. In: Proceedings of the 18th International Conference on World Wide Web, pp. 721–730 (2009)
Chung, F., Chung, F.R.K., Graham, F.C., Lu, L., Chung, K.F., et al.: Complex graphs and networks. Am. Math. Soc. (2006)
Clauset, A., Shalizi, C.R., Newman, M.E.J.: Power-law distributions in empirical data. SIAM Rev. 51(4), 661–703 (2009)
Erdős, P., Rényi, A.: On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci 5(1), 17–60 (1960)
Gabielkov, M., Legout, A.: The complete picture of the Twitter social graph. In: Proceedings on CoNEXT Student Workshop, pp. 19–20. ACM (2012)
Ghoshal, G., Newman, M.E.J.: Growing distributed networks with arbitrary degree distributions. Eur. Phys. J. B 58(2), 175–184 (2007)
Giroire, F., Pérennes, S., Trolliet, T.: A random growth model with any real or theoretical degree distribution. arXiv preprint arXiv:2008.03831 (2020)
Gjoka, M., Kurant, M., Butts, C.T., Markopoulou, A.: Walking in Facebook: a case study of unbiased sampling of OSNs. In: IEEE INFOCOM (2010)
Jóhannesson, G., Björnsson, G., Gudmundsson, E.H.: Afterglow light curves and broken power laws: a statistical study. Astrophys. J. Lett. 640(1), L5 (2006)
Leskovec, J., Horvitz, E.: Planetary-scale views on a large instant-messaging network. In: Proceedings of the 17th International Conference on World Wide Web (2008)
Lima-Mendez, G., van Helden, J.: The powerful law of the power law and other myths in network biology. Mol. BioSyst. 5(12), 1482–1493 (2009)
Myers, S.A., Sharma, A., Gupta, P., Lin, J.: Information network or social network?: The structure of the Twitter follow graph. In: Proceedings of the 23rd International Conference on World Wide Web, pp. 493–498. ACM (2014)
Newman, M.E.J., Strogatz, S.H., Watts, D.J.: Random graphs with arbitrary degree distributions and their applications. Phys. Rev. E 64, 026118 (2001)
Pržulj, N.: Biological network comparison using graphlet degree distribution. Bioinformatics 23(2), e177–e183 (2007)
Sallaberry, A., Zaidi, F., Melançon, G.: Model for generating artificial social networks having community structures with small-world and scale-free properties. Soc. Netw. Anal. Min. 3(3), 597–609 (2013)
Seshadri, M., Machiraju, S., Sridharan, A., Bolot, J., Faloutsos, C., Leskove, J.: Mobile call graphs: beyond power-law and lognormal distributions. In: ACM SIGKDD, pp. 596–604 (2008)
Stephen, A.T., Toubia, O.: Explaining the power-law degree distribution in a social commerce network. Soc. Netw. 31(4), 262–270 (2009)
Trolliet, T., Cohen, N., Giroire, F., Hogie, L., Pérennes, S.: Interest clustering coefficient: a new metric for directed networks like Twitter. arXiv preprint arXiv:2008.00517 (2020)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Giroire, F., Pérennes, S., Trolliet, T. (2021). A Random Growth Model with Any Real or Theoretical Degree Distribution. In: Benito, R.M., Cherifi, C., Cherifi, H., Moro, E., Rocha, L.M., Sales-Pardo, M. (eds) Complex Networks & Their Applications IX. COMPLEX NETWORKS 2020 2020. Studies in Computational Intelligence, vol 944. Springer, Cham. https://doi.org/10.1007/978-3-030-65351-4_35
Download citation
DOI: https://doi.org/10.1007/978-3-030-65351-4_35
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-65350-7
Online ISBN: 978-3-030-65351-4
eBook Packages: EngineeringEngineering (R0)