NDlib: a python library to model and analyze diffusion processes over complex networks

  • Giulio RossettiEmail author
  • Letizia Milli
  • Salvatore Rinzivillo
  • Alina Sîrbu
  • Dino Pedreschi
  • Fosca Giannotti


Nowadays the analysis of dynamics of and on networks represents a hot topic in the social network analysis playground. To support students, teachers, developers and researchers, in this work we introduce a novel framework, namely NDlib, an environment designed to describe diffusion simulations. NDlib is designed to be a multi-level ecosystem that can be fruitfully used by different user segments. For this reason, upon NDlib, we designed a simulation server that allows remote execution of experiments as well as an online visualization tool that abstracts its programmatic interface and makes available the simulation platform to non-technicians.


Social network analysis software Epidemics Opinion dynamics 



This work is funded by the European Community’s H2020 Program under the funding scheme “FETPROACT-1-2014: Global Systems Science (GSS),” grant agreement # 641191 CIMPLEX “Bringing CItizens, Models and Data together in Participatory, Interactive SociaL EXploratories” (CIMPLEX: This work is supported by the European Community’s H2020 Program under the scheme “INFRAIA-1-2014-2015: Research Infrastructures", grant agreement #654024 “SoBigData: Social Mining & Big Data Ecosystem" (SoBigData:

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest


  1. 1.
    Ahrenberg, L., Kok, S., Vasarhelyi, K., Rutherford, A.: Nepidemix (2016)Google Scholar
  2. 2.
    Van den Broeck, W., Gioannini, C., Gonçalves, B., Quaggiotto, M., Colizza, V., Vespignani, A.: The gleamviz computational tool, a publicly available software to explore realistic epidemic spreading scenarios at the global scale. BMC Infect Dis 11(1), 37 (2011)CrossRefGoogle Scholar
  3. 3.
    Burt, R.S.: Social contagion and innovation: cohesion versus structural equivalence. Am. J. Sociol. 92, 1287 (1987)CrossRefGoogle Scholar
  4. 4.
    Casteigts, A., Flocchini, P., Quattrociocchi, W., Santoro, N.: Time-varying graphs and dynamic networks. Int. J. Parallel Emerg. Distrib. Syst. 27(5), 387–408 (2012)CrossRefGoogle Scholar
  5. 5.
    Castellano, C., Munoz, M.A., Pastor-Satorras, R.: The non-linear q-voter model. Phys. Rev. E 80, 041–129 (2009)CrossRefGoogle Scholar
  6. 6.
    Chao, D.L., Halloran, M.E., Obenchain, V.J., Longini Jr., I.M.: Flute, a publicly available stochastic influenza epidemic simulation model. PLoS Comput. Biol. 6(1), e1000–656 (2010)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Clifford, P., Sudbury, A.: A model for spatial conflict. Biometrika 60(3), 581–588 (1973). MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Coelho, F.C., Cruz, O.G., Codeço, C.T.: Epigrass: a tool to study disease spread in complex networks. Sour. Code Biol. Med. 3(1), 3 (2008)CrossRefGoogle Scholar
  9. 9.
    Deffuant, G., Neau, D., Amblard, F., Weisbuch, G.: Mixing beliefs among interacting agents. Adv. Complex Syst. 3(4), 87–98 (2000)CrossRefGoogle Scholar
  10. 10.
    Friedman, R., Friedman, M.: The Tyranny of the Status Quo. Harcourt Brace Company, Orlando (1984)Google Scholar
  11. 11.
    Galam, S.: Minority opinion spreading in random geometry. Eur. Phys. J. B 25(4), 403–406 (2002)Google Scholar
  12. 12.
    Granovetter, M.: Threshold models of collective behavior. Am. J. Sociol. 83(6), 1420–1443 (1978)CrossRefGoogle Scholar
  13. 13.
    Grefenstette, J.J., Brown, S.T., Rosenfeld, R., DePasse, J., Stone, N.T., Cooley, P.C., Wheaton, W.D., Fyshe, A., Galloway, D.D., Sriram, A., et al.: Fred (a framework for reconstructing epidemic dynamics): an open-source software system for modeling infectious diseases and control strategies using census-based populations. BMC Public Health 13(1), 940 (2013)CrossRefGoogle Scholar
  14. 14.
    Havlin, S.: Phone infections. Science 324, 1023 (2009)CrossRefGoogle Scholar
  15. 15.
    Holley, R., Liggett, T.: Ergodic theorems for weakly interacting infinite systems and the voter model. Ann. Probab. 3(4), 643–663 (1975)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Holme, P., Saramäki, J.: Temporal networks. Phys. Rep. 519(3), 97–125 (2012)CrossRefGoogle Scholar
  17. 17.
    Jenness, S., Goodreau, S.M., Morris, M.: Epimodel: Mathematical modeling of infectious disease. r package version 1.3.0. (2017).
  18. 18.
    Kempe, D., Kleinberg, J., Tardos, E.: Maximizing the spread of influence through a social network. In: Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’03, pp. 137–146 (2003)Google Scholar
  19. 19.
    Kermack, W.O., McKendrick, A.: A contribution to the mathematical theory of epidemics. Proceed. R. Soc. Lond. Ser. A Contain. Papers Math. Phys. Character 115(772), 700–721 (1927)CrossRefzbMATHGoogle Scholar
  20. 20.
    Kiss, I.Z., Miller, J.C., Simon, P.: Mathematics of Epidemics on Networks: From Exact to Approximate Models. Springer (Forthcoming)Google Scholar
  21. 21.
    Kovanen, L., Karsai, M., Kaski, K., Kertész, J., Saramäki, J.: Temporal motifs in time-dependent networks. J. Statist. Mech. Theory Exp. 2011(11), p11005 (2011)CrossRefGoogle Scholar
  22. 22.
    Krapivsky, P.L., Redner, S., Ben-Naim, E.: A Kinetic View of Statistical Physics. Cambridge University Press, Cambridge (2010)CrossRefzbMATHGoogle Scholar
  23. 23.
    Lee, S., Rocha, L.E., Liljeros, F., Holme, P.: Exploiting temporal network structures of human interaction to effectively immunize populations. PLoS ONE 7(5), e36–439 (2012)Google Scholar
  24. 24.
    Leskovec, J., Sosič, R.: Snap: a general-purpose network analysis and graph-mining library. ACM Trans. Intell. Syst. Technol. (TIST) 8(1), 1 (2016)CrossRefGoogle Scholar
  25. 25.
    Milli, L., Rossetti, G., Pedreschi, D., Giannotti, F.: Information diffusion in complex networks: The active/passive conundrum. In: Complex Networks (2017)Google Scholar
  26. 26.
    Milli, L., Rossetti, G., Pedreschi, D., Giannotti, F.: Diffusive phenomena in dynamic networks: a data-driven study. In: 9th Conference on Complex Networks, CompleNet (2018)Google Scholar
  27. 27.
    Newton, C.M.: Graphics: from alpha to omega in data analysis. In: Wang, P.C. (ed.) Graphical Representation of Multivariate Data, pp. 59–92. Academic Press (1978). URL
  28. 28.
    Pennacchioli, D., Rossetti, G., Pappalardo, L., Pedreschi, D., Giannotti, F., Coscia, M.: The three dimensions of social prominence. In: International Conference on Social Informatics, pp. 319–332. Springer (2013)Google Scholar
  29. 29.
    Rossetti, G.: Rdyn: graph benchmark handling community dynamics. J. Complex Netw. 5, 893 (2017)CrossRefGoogle Scholar
  30. 30.
    Rossetti, G., Cazabet, R.: Community discovery in dynamic networks: a survey. arXiv preprint arXiv:1707.03186 (2017)
  31. 31.
    Rossetti, G., Guidotti, R., Miliou, I., Pedreschi, D., Giannotti, F.: A supervised approach for intra-/inter-community interaction prediction in dynamic social networks. Soc. Netw. Anal. Min. 6(1), 86 (2016)CrossRefGoogle Scholar
  32. 32.
    Rossetti, G., Pappalardo, L., Pedreschi, D., Giannotti, F.: Tiles: an online algorithm for community discovery in dynamic social networks. Mach. Learn. pp. 1–29 (2016)Google Scholar
  33. 33.
    Ruan, Z., Iñiguez, G., Karsai, M., Kertész, J.: Kinetics of social contagion. Phys. Rev. Lett 115, 218702 (2015). CrossRefGoogle Scholar
  34. 34.
    Sahneh, F.D., Vajdi, A., Shakeri, H., Fan, F., Scoglio, C.: Gemfsim: a stochastic simulator for the generalized epidemic modeling framework. J. Comput. Sci. 22, 36–44 (2017)CrossRefGoogle Scholar
  35. 35.
    Sîrbu, A., Loreto, V., Servedio, V.D., Tria, F.: Opinion dynamics with disagreement and modulated information. J. Stat. Phys. 151, 1–20 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Sîrbu, A., Loreto, V., Servedio, V.D., Tria, F.: Opinion dynamics: models, extensions and external effects. In: Participatory Sensing, Opinions and Collective Awareness, pp. 363–401. Springer International Publishing (2017)Google Scholar
  37. 37.
    Sznajd-Weron, K., Sznajd, J.: Opinion evolution in closed community. Int. J. Mod. Phys. C 11, 1157–1165 (2001)CrossRefzbMATHGoogle Scholar
  38. 38.
    Szor, P.: Fighting Computer Virus Attacks. USENIX, Berkeley (2004)Google Scholar
  39. 39.
    Tabourier, L., Libert, A.S., Lambiotte, R.: Predicting links in ego-networks using temporal information. EPJ Data Sci. 5(1), 1 (2016)CrossRefGoogle Scholar
  40. 40.
    Viard, T., Latapy, M., Magnien, C.: Computing maximal cliques in link streams. Theor. Comput. Sci. 609, 245–252 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    Vilone, D., Giardini, F., Paolucci, M., Conte, R.: Reducing individuals’ risk sensitiveness can promote positive and non-alarmist views about catastrophic events in an agent-based simulation. arXiv preprint arXiv:1609.04566 (2016)
  42. 42.
    Wang, P., González, M.C., Menezes, R., Barabási, A.L.: Understanding the spread of malicious mobile-phone programs and their damage potential. Int. J. Inf. Secur. 12, 383 (2013)CrossRefGoogle Scholar
  43. 43.
    Watts, D.J.: A simple model of global cascades on random networks. Proc. Natl. Acad. Sci. 99(9), 5766–5771 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  44. 44.
    Wilensky, U.: Netlogo (1999)Google Scholar
  45. 45.
    Word, D.P., Abbott, G.H., Cummings, D., Laird, C.D.: Estimating seasonal drivers in childhood infectious diseases with continuous time and discrete-time models. In: American Control Conference (ACC), 2010, pp. 5137–5142. IEEE (2010)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.University of Pisa2 PisaItaly
  2. 2.KDD Lab. ISTI-CNR1 PisaItaly

Personalised recommendations