Novel Edge and Density Metrics for Link Cohesion

  • Cetin Savkli
  • Catherine Schwartz
  • Amanda GalanteEmail author
  • Jonathan Cohen
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 881)


We present a new metric of link cohesion for measuring the strength of edges in complex, highly connected graphs. Link cohesion accounts for local small hop connections and associated node degrees and can be used to support edge scoring and graph simplification. We also present a novel graph density measure to estimate the average cohesion across nodes. Link cohesion and the density measure are employed to demonstrate community detection through graph sparsification by maximizing graph density. Link cohesion is also shown to be loosely correlated with edge betweenness centrality.


Link cohesion Graph sparsification Graph density Centrality Community detection 



This work was supported by internal research and development funding provided by Johns Hopkins University Applied Physics Laboratory. Algorithms were implemented with SOCRATES [23] and visualized with an internal tool, Pointillist.


  1. 1.
    Bai, L., Liang, J., Du, H., Guo, Y.: A novel community detection algorithm based on simplification of complex networks. Knowl.-Based Syst. 143, 58–64 (2018)CrossRefGoogle Scholar
  2. 2.
    Blondel, V., Guillaume, J., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in large networks. J. Stat. Mech.: Theory Exp. 2008(10), P10008 (2008)CrossRefGoogle Scholar
  3. 3.
    Cohen, J.: Trusses: Cohesive subgraphs for social network analysis. Natl. Secur. Agency Tech. Rep. 16, 1–3 (2008) Google Scholar
  4. 4.
    Cohen, J.: Graph twiddling in a mapreduce world. Comput. Sci. Eng. 11(4), 29 (2009)CrossRefGoogle Scholar
  5. 5.
    Cohen, J.: Trusses and trapezes: easily-interpreted communities in social networks. arXiv, abs/1907.09417 (2019)Google Scholar
  6. 6.
    De Meo, P., Ferrara, E., Fiumara, G., Ricciardello, A.: A novel measure of edge centrality in social networks. Knowl.-Based Syst. 30, 136–150 (2012)CrossRefGoogle Scholar
  7. 7.
    Fortunato, S.: Community detection in graphs. Phys. Rep. 486(3–5), 75–174 (2010) MathSciNetCrossRefGoogle Scholar
  8. 8.
    Freeman, L.: Lin Freeman’s network data collection.
  9. 9.
    Freeman, L.: A set of measures of centrality based on betweenness. Sociometry 40(1), 35–41 (1977)CrossRefGoogle Scholar
  10. 10.
    Girvan, M., Newman, M.: Community structure in social and biological networks. PNAS 99(12), 7821–7826 (2002)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Glattfelder, J.: Backbone of complex networks of corporations: the flow of control. In: Decoding Complexity, pp. 67–93. Springer (2013)Google Scholar
  12. 12.
    Harel, J., Koch, C., Perona, P.: Graph-based visual saliency. In: Advances in Neural Information Processing Systems, pp. 545–552 (2007)Google Scholar
  13. 13.
    Lancichinetti, A., Fortunato, S., Radicchi, F.: Benchmark graphs for testing community detection algorithms. Phys. Rev. E 78(4), 046110 (2008)CrossRefGoogle Scholar
  14. 14.
    Leskovec, J., Kleinberg, J., Faloutsos, C.: Graph evolution: densification and shrinking diameters. ACM Trans. Knowl. Discov. Data (TKDD) 1(1), 2 (2007)CrossRefGoogle Scholar
  15. 15.
    Leskovec, J., Krevl, A.: SNAP Datasets: Stanford large network dataset collection, June 2014.
  16. 16.
    Marsden, P.: Egocentric and sociocentric measures of network centrality. Soc. Netw. 24(4), 407–422 (2002)CrossRefGoogle Scholar
  17. 17.
    Moody, J.: Peer influence groups: identifying dense clusters in large networks. Soc. Netw. 23(4), 261–283 (2001)CrossRefGoogle Scholar
  18. 18.
    Newman, M.: Analysis of weighted networks. Phys. Rev. E 70(5), 056131 (2004)CrossRefGoogle Scholar
  19. 19.
    Newman, M.: Modularity and community structure in networks. PNAS 103(23), 8577–8582 (2006)CrossRefGoogle Scholar
  20. 20.
    Paranjape, A., Benson, A., Leskovec, J.: Motifs in temporal networks. In: Proceedings of the Tenth ACM International Conference on Web Search and Data Mining, pp. 601–610. ACM (2017)Google Scholar
  21. 21.
    Porter, M., Onnela, J., Mucha, P.: Communities in networks. Not. AMS 56(9), 1082–1097 (2009)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Satuluri, V., Parthasarathy, S., Ruan, Y.: Local graph sparsification for scalable clustering. In: Proceedings of the 2011 ACM SIGMOD International Conference on Management of Data, pp. 721–732. ACM (2011)Google Scholar
  23. 23.
    Savkli, C., Carr, R., Chapman, M., Chee, B., Minch, D.: Socrates: a system for scalable graph analytics. In: IEEE HPEC 2014, pp. 1–6 (2014)Google Scholar
  24. 24.
    Savkli, C., Lin, J., Graff, P., Kinsey, M.: Galileo: a generalized low-entropy mixture model. In: DMIN 2017, pp. 58–64 (2017)Google Scholar
  25. 25.
    Tumminello, M., Aste, T., Di Matteo, T., Mantegna, R.: A tool for filtering information in complex systems. PNAS 102(30), 10421–10426 (2005)CrossRefGoogle Scholar
  26. 26.
    Zachary, W.: An information flow model for conflict and fission in small groups. J. Anthropol. Res. 33(4), 452–473 (1977)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Cetin Savkli
    • 1
  • Catherine Schwartz
    • 1
  • Amanda Galante
    • 1
    Email author
  • Jonathan Cohen
    • 1
  1. 1.Johns Hopkins University Applied Physics LaboratoryLaurelUSA

Personalised recommendations