Newton’s Gravitational Law for Link Prediction in Social Networks

  • Akanda Wahid -Ul- AshrafEmail author
  • Marcin Budka
  • Katarzyna Musial-Gabrys
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 689)


Link prediction is an important research area in network science due to a wide range of real-world application. There are a number of link prediction methods. In the area of social networks, these methods are mostly inspired by social theory, such as having more mutual friends between two people in a social network platform entails higher probability of those two people becoming friends in the future. In this paper we take our inspiration from a different area, which is Newton’s law of universal gravitation. Although this law deals with physical bodies, based on our intuition and empirical results we found that this could also work in networks, and especially in social networks. In order to apply this law, we had to endow nodes with the notion of mass and distance. While node importance could be considered as mass, the shortest path, path count, or inverse similarity (AdamicAdar, Katz score etc.) could be considered as distance. In our analysis, we have primarily used degree centrality to denote the mass of the nodes, while the lengths of shortest paths between them have been used as distances. In this study we compare the proposed link prediction approach to 7 other methods on 4 datasets from various domains. To this end, we use the ROC curves and the AUC measure to compare the methods. As the results show that our approach outperforms the other 7 methods on 2 out of the 4 datasets, we also discuss the potential reasons of the observed behaviour.


  1. 1.
    Adamic, L.A., Adar, E.: Friends and neighbors on the web. Soc. Netw. 25(3), 211–230 (2003)CrossRefGoogle Scholar
  2. 2.
    Airoldi, E.M., Blei, D.M., Fienberg, S.E., Xing, E.P., Jaakkola, T.: Mixed membership stochastic block models for relational data with application to protein-protein interactions. In: Proceedings of the International Biometrics Society Annual Meeting, pp. 1–34 (2006)Google Scholar
  3. 3.
    Al Hasan, M., Zaki, M.J.: A survey of link prediction in social networks. In: Social Network Data Analytics, pp. 243–275, Springer (2011)Google Scholar
  4. 4.
    Al Hasan, M., Chaoji, V., Salem, S., Zaki, M.: Link prediction using supervised learning. In: SDM06: Workshop on Link Analysis, Counter-Terrorism and Security (2006)Google Scholar
  5. 5.
    Backstrom, L., Boldi, P., Rosa, M., Ugander, J., Vigna, S.: Four degrees of separation. In: Proceedings of the 4th Annual ACM Web Science Conference, ACM, pp. 33–42 (2012)Google Scholar
  6. 6.
    Barabâsi, A.L., Jeong, H., Néda, Z., Ravasz, E., Schubert, A., Vicsek, T.: Evolution of the social network of scientific collaborations. Physica A 311(3), 590–614 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Barzel, B., Barabási, A.L.: Network link prediction by global silencing of indirect correlations. Nat. Biotechnol. 31(8), 720–725 (2013)CrossRefGoogle Scholar
  8. 8.
    Bliss, C.A., Frank, M.R., Danforth, C.M., Dodds, P.S.: An evolutionary algorithm approach to link prediction in dynamic social networks. J. Comput. Sci. 5(5), 750–764 (2014)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Brin, S., Page, L.: Reprint of: The anatomy of a large-scale hypertextual web search engine. Comput. Netw. 56(18), 3825–3833 (2012)CrossRefGoogle Scholar
  10. 10.
    Cannistraci, C.V., Alanis-Lobato, G., Ravasi, T.: Minimum curvilinearity to enhance topological prediction of protein interactions by network embedding. Bioinformatics 29(13), i199–i209 (2013)CrossRefGoogle Scholar
  11. 11.
    Chaintreau, A., Hui, P., Crowcroft, J., Diot, C., Gass, R., Scott, J.: Impact of human mobility on opportunistic forwarding algorithms. IEEE Trans. Mob. Comput. 6(6) (2007)Google Scholar
  12. 12.
    Crombie, A.: Newton’s conception of scientific method. Phys. Bull. 8(11), 350 (1957)CrossRefGoogle Scholar
  13. 13.
    Csardi, G., Nepusz, T.: The igraph software package for complex network research. Int. J. Comp. Syst. 1695(5), 1–9 (2006)Google Scholar
  14. 14.
    Davis, J., Goadrich, M.: The relationship between precision-recall and roc curves. In: Proceedings of the 23rd International Conference on Machine Learning, ACM, pp. 233–240 (2006)Google Scholar
  15. 15.
    Edunov, S., Diuk, C., Filiz, I.O., Bhagat, S., Burke, M.: Three and a half degrees of separation. Research at Facebook (2016)Google Scholar
  16. 16.
    Gerard, S., Michael, J.M.: Introduction to Modern Information Retrieval. McGraw-Hill, New York (1983)zbMATHGoogle Scholar
  17. 17.
    Hristova, D., Noulas, A., Brown, C., Musolesi, M., Mascolo, C.: A multilayer approach to multiplexity and link prediction in online geo-social networks. EPJ Data Science 5(1), 24 (2016)CrossRefGoogle Scholar
  18. 18.
    Isella, L., Stehlé, J., Barrat, A., Cattuto, C., Pinton, J.F., Van den Broeck, W.: What’s in a crowd? analysis of face-to-face behavioral networks. J. Theor. Biol. 271(1), 166–180 (2011)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Juszczyszyn, K., Musial, K., Budka, M.: Link prediction based on subgraph evolution in dynamic social networks. In: Privacy, Security, Risk and Trust (PASSAT) and 2011 IEEE Third International Conference on Social Computing (SocialCom), pp. 27–34, IEEE (2011)Google Scholar
  20. 20.
    Katz, L.: A new status index derived from sociometric analysis. Psychometrika 18(1), 39–43 (1953)CrossRefzbMATHGoogle Scholar
  21. 21.
    Krioukov, D., Kitsak, M., Sinkovits, R.S., Rideout, D., Meyer, D., Boguñá, M.: Network cosmology. Scientific reports 2 (2012)Google Scholar
  22. 22.
    Kunegis, J.: arxiv hep-th network dataset konect (2013). Accessed April 2017
  23. 23.
    Kunegis, J.: Haggle network dataset konect (2013). Accessed April 2017
  24. 24.
    Kunegis, J.: Hypertext 2009 network dataset konect (2013). Accessed April 2017
  25. 25.
    Kunegis, J.: Konect: the koblenz network collection. In: Proceedings of the 22nd International Conference on World Wide Web, ACM, pp. 1343–1350 (2013)Google Scholar
  26. 26.
    Landherr, A., Friedl, B., Heidemann, J.: A critical review of centrality measures in social networks. Bus. Inf. Syst. Eng. 2(6), 371–385 (2010)CrossRefGoogle Scholar
  27. 27.
    Leskovec, J., Kleinberg, J., Faloutsos, C.: Graph evolution: Densification and shrinking diameters. ACM Trans. Knowl. Disc. Data (TKDD) 1(1), 2 (2007)CrossRefGoogle Scholar
  28. 28.
    Li, J., Zhang, L., Meng, F., Li, F.: Recommendation algorithm based on link prediction and domain knowledge in retail transactions. Procedia Comput. Sci. 31, 875–881 (2014)CrossRefGoogle Scholar
  29. 29.
    Liben-Nowell, D., Kleinberg, J.: The link-prediction problem for social networks. J. Assoc. Inform. Sci. Technol. 58(7), 1019–1031 (2007)CrossRefGoogle Scholar
  30. 30.
    Lichtenwalter, R.N., Chawla, N.V.: Lpmade: Link prediction made easy. J. Mach. Learn. Res. 12:2489–2492 (2011)Google Scholar
  31. 31.
    Lichtenwalter, R.N., Lussier, J.T., Chawla, N.V.: New perspectives and methods in link prediction. In: Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, ACM, pp. 243–252 (2010)Google Scholar
  32. 32.
    Mori, J., Kajikawa, Y., Kashima, H., Sakata, I.: Machine learning approach for finding business partners and building reciprocal relationships. Expert Syst. Appl. 39(12):10402–10407 (2012)Google Scholar
  33. 33.
    Newman, M.E.: Clustering and preferential attachment in growing networks. Phys. Rev. E 64(2):025–102 (2001)Google Scholar
  34. 34.
    Newton, I.: Philosophiæ naturalis principia mathematica (mathematical principles of natural philosophy). London (1687) (1987)Google Scholar
  35. 35.
    Pandey, V.S., Kumar, R., Singh, P.: An optimized all pair shortest paths algorithm. Int. J. Comput. Appl. 2(3), 0975–8887 (2010)Google Scholar
  36. 36.
    Panzarasa, P., Opsahl, T., Carley, K.M.: Patterns and dynamics of users’ behavior and interaction: Network analysis of an online community. J. Assoc. Inform. Sci. Technol. 60(5), 911–932 (2009)CrossRefGoogle Scholar
  37. 37.
    Papadopoulos, F., Kitsak, M., Serrano, M.Á., Boguñá, M., Krioukov, D.: Popularity versus similarity in growing networks. Nature 489, 537–540 (2012)CrossRefGoogle Scholar
  38. 38.
    Raeder, T., Lizardo, O., Hachen, D., Chawla, N.V.: Predictors of short-term decay of cell phone contacts in a large scale communication network. Soc. Netw. 33(4), 245–257 (2011)CrossRefGoogle Scholar
  39. 39.
    Robin, X., Turck, N., Hainard, A., Tiberti, N., Lisacek, F., Sanchez, J.C., Müller, M.: Proc: an open-source package for r and s+ to analyze and compare roc curves. BMC bioinformatics 12(1), 77 (2011)CrossRefGoogle Scholar
  40. 40.
    Tan, R., Gu, J., Chen, P., Zhong, Z.: Link prediction using protected location history. In: 2013 Fifth International Conference on Computational and Information Sciences (ICCIS), pp. 795–798. IEEE (2013)Google Scholar
  41. 41.
    Thorup, M.: Undirected single-source shortest paths with positive integer weights in linear time. J. ACM (JACM) 46(3), 362–394 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    Thorup, M.: Floats, integers, and single source shortest paths. J. Algorithms 35(2), 189–201 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Travers, J., Milgram, S.: The small world problem. Phychology Today. 1, 61–67 (1967)Google Scholar
  44. 44.
    Wang, P., Xu, B., Wu, Y., Zhou, X.: Link prediction in social networks: the state-of-the-art. Sci. China Inform. Sci. 58(1), 1–38 (2015)Google Scholar
  45. 45.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393(6684), 440–442 (1998)CrossRefzbMATHGoogle Scholar
  46. 46.
    Wu, S., Sun, J., Tang, J.: Patent partner recommendation in enterprise social networks. In: Proceedings of the sixth ACM International Conference on Web Search and Data Mining, ACM, pp. 43–52 (2013)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Akanda Wahid -Ul- Ashraf
    • 1
    Email author
  • Marcin Budka
    • 1
  • Katarzyna Musial-Gabrys
    • 2
  1. 1.Department of Computing and InformaticsBournemouth UniversityPooleUK
  2. 2.School of SoftwareUniversity of Technology SydneySydneyAustralia

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