Mathematical Analysis of a Network’s Asymptotic Behaviour Based on Its Strongly Connected Components

  • Jan TreurEmail author
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 812)


In this paper a general theorem is presented that relates asymptotic behaviour of a network to the network’s characteristics concerning the network’s strongly connected components and their mutual connections. The theorem generalises existing theorems for specific cases such as acyclic networks, fully and strongly connected networks, and theorems addressing only linear functions.


  1. 1.
    Bloem, R., Gabow, H.N., Somenzi, F.: An algorithm for strongly connected component analysis in n log n symbolic steps. Form. Meth. Syst. Des. 28, 37–56 (2006)Google Scholar
  2. 2.
    Bosse, T., Duell, R., Memon, Z.A., Treur, J., van der Wal, C.N.: Agent-based modelling of emotion contagion in groups. Cogn. Comput. 7(1), 111–136 (2015)Google Scholar
  3. 3.
    Chen, Y.: General spanning trees and reachability query evaluation. In: Desai, B.C. (ed.) Proceedings of the 2nd Canadian Conference on Computer Science and Software Engineering, C3S2E’09, pp. 243–252. ACM Press (2009)Google Scholar
  4. 4.
    Fleischer, L.K., Hendrickson, B., Pınar, A.: On identifying strongly connected components in parallel. In: Rolim J. (ed) Parallel and Distributed Processing. IPDPS 2000. Lecture Notes in Computer Science, vol. 1800, pp. 505–511. Springer (2000)Google Scholar
  5. 5.
    Gentilini, R., Piazza, C., Policriti, A.: Computing strongly connected components in a linear number of symbolic steps. In: Proceedings of the SODA’03, pp. 573–582 (2003)Google Scholar
  6. 6.
    Harary, F., Norman, R.Z., Cartwright, D.: Structural models: an introduction to the theory of directed graphs. Wiley, New York (1965)Google Scholar
  7. 7.
    Kuich, W.: On the entropy of context-free languages. Inf. Control 16, 173–200 (1970)Google Scholar
  8. 8.
    Li, G., Zhu, Z., Cong, Z., Yang, F.: Efficient decomposition of strongly connected components on GPUs. J. Syst. Architect. 60(1), 1–10 (2014)Google Scholar
  9. 9.
    Tarjan, R.: Depth-first search and linear graph algorithms. SIAM J. Comput. 1(2), 146–160 (1972)Google Scholar
  10. 10.
    Treur, J.: Network-Oriented Modeling: Addressing the Complexity of Cognitive, Affective and Social Interactions. Springer Publishers (2016)Google Scholar
  11. 11.
    Treur, J.: The Ins and Outs of Network-Oriented Modeling: from Biological Networks and Mental Networks to Social Networks and Beyond. Paper for Keynote Lecture at ICCCI’18. Springer Publishers (2018)Google Scholar
  12. 12.
    Treur, J.: Relating emerging network behaviour to network structure. In: Proceedings of the 7th International Conference on Complex Networks and their Applications, ComplexNetworks’18. Studies in Computational Intelligence, Springer (2018)Google Scholar
  13. 13.
    Wijs, A., Katoen, J.P., Bošnacki, D.: Efficient GPU algorithms for parallel decomposition of graphs into strongly connected and maximal end components. Form. Methods Syst. Des. 48, 274–300 (2016)Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Behavioural Informatics GroupVrije Universiteit AmsterdamAmsterdamThe Netherlands

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