Skip to main content
Springer Nature Link
Log in

Correlations between characteristics of maximum influence and degree distributions in software networks

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

Software systems can be represented as complex networks and their artificial nature can be investigated with approaches developed in network analysis. Influence maximization has been successfully applied on software networks to identify the important nodes that have the maximum influence on the other parts. However, research is open to study the effects of network fabric on the influence behavior of the highly influential nodes. In this paper, we construct class dependence graph (CDG) networks based on eight practical Java software systems, and apply the procedure of influence maximization to study empirically the correlations between the characteristics of maximum influence and the degree distributions in the software networks. We demonstrate that the artificial nature of CDG networks is reflected partly from the scale free behavior: the in-degree distribution follows power law, and the out-degree distribution is lognormal. For the influence behavior, the expected influence spread of the maximum influence set identified by the greedy method correlates significantly with the degree distributions. In addition, the identified influence set contains influential classes that are complex in both the number of methods and the lines of code (LOC). For the applications in software engineering, the results provide possibilities of new approaches in designing optimization procedures of software systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Myers C R. Software systems as complex networks: structure, function, and evolvability of software collaboration graphs. Phys Rev E, 2003, 68: 046116

    Article  Google Scholar 

  2. Jenkins S, Kirk S R. Software architecture graphs as complex networks: a novel partitioning scheme to measure stability and evolution. Inform Sciences, 2007, 177: 2587–2601

    Article  Google Scholar 

  3. Zheng X, Zeng D, Li H, et al. Analyzing open-source software systems as complex networks. Physica A, 2008, 387: 6190–6200

    Article  Google Scholar 

  4. Cai K Y, Yin B B. Software execution processes as an evolving complex network. Inform Sciences, 2009, 179: 1903–1928

    Article  Google Scholar 

  5. De Moura A P S, Lai Y C, Motter A E. Signatures of small-world and scale-free properties in large computer programs. Phys Rev E, 2003, 68: 017102

    Article  Google Scholar 

  6. Concas G, Marchesi M, Pinna S, et al. Power-laws in a large object-oriented software system. IEEE Trans Softw Eng, 2007, 33: 687–708

    Article  Google Scholar 

  7. Maillart T, Sornette D, Spaeth S, et al. Empirical tests of Zipf’s law mechanism in open source linux distribution. Phys Rev Lett, 2008, 101: 218701

    Article  Google Scholar 

  8. Kohring G A. Complex dependencies in large software systems. Adv Complex Syst, 2009, 12: 565–581

    Article  MATH  Google Scholar 

  9. Chepelianskii A D. Towards physical laws for software architecture. arXiv: 1003.5455, 2010

    Google Scholar 

  10. Šubelj L, Bajec M. Community structure of complex software systems: analysis and applications. Physica A, 2011, 390: 2968–2975

    Article  Google Scholar 

  11. LaBelle N, Wallingford E. Inter-package dependency networks in open-source software. arXiv:0411096, 2004

    Google Scholar 

  12. Yang F, Lv J, Mei H. Technical framework for Internetware: an architecture centric approach. Sci China Ser F-Inf Sci, 2008, 51: 610–622

    Article  Google Scholar 

  13. Mei H, Huang G, Lan L, et al. A software architecture centric self-adaptation approach for Internetware. Sci China Ser F-Inf Sci, 2008, 51: 722–742

    Article  MATH  Google Scholar 

  14. Lv J, Ma X, Tao X P, et al. On environment-driven software model for Internetware. Sci China Ser F-Inf Sci, 2008, 51: 683–721

    Google Scholar 

  15. Valverde S, Solé R V. Hierarchical small-worlds in software architecture. arXiv:0307278, 2007

    Google Scholar 

  16. Strogatz S H. Exploring complex networks. Nature, 2001, 410: 268–276

    Article  Google Scholar 

  17. Albert R, Barabási A L. Statistical mechanics of complex networks. Rev Mod Phys, 2002, 74: 47–97

    Article  MATH  Google Scholar 

  18. Bhattacharya P, Iliofotou M, Neamtiu I, et al. Graph-based analysis and prediction for software evolution. In: Proceedings of the International Conference on Software Engineering, Zurich, 2012. 419–429

    Google Scholar 

  19. Newman M E J. The structure and function of complex networks. SIAM Rev, 2003, 45: 167–256

    Article  MATH  MathSciNet  Google Scholar 

  20. Concas G, Marchesi M, Pinna S, et al. On the suitability of yule process to stochastically model some properties of object-oriented systems. Physica A, 2006, 370: 817–831

    Article  Google Scholar 

  21. Louridas P, Spinellis D, Vlachos V. Power laws in software. ACM Trans Softw Eng Meth, 2008, 18: 2

    Article  Google Scholar 

  22. Kitsak M, Gallos L K, Havlin S, et al. Identification of influential spreaders in complex networks. Nat Phys, 2010, 6: 888–893

    Article  Google Scholar 

  23. Kimura M, Saito K, Nakano R, et al. Extracting influential nodes on a social network for information diffusion. Data Min Knowl Disc, 2010, 20: 70–97

    Article  MathSciNet  Google Scholar 

  24. Lu Z, Zhang W, Wu W, et al. The complexity of influence maximization problem in the deterministic linear threshold model. J Comb Optim, 2012, 24: 374–378

    Article  MATH  MathSciNet  Google Scholar 

  25. Kempe D, Kleinberg J, Tardos E. Maximizing the spread of influence through a social network. In: Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Washington, 2003. 137–146

    Google Scholar 

  26. Richardson M, Domingos P. Mining knowledge-sharing sites for viral marketing. In: Proceedings of the 8th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Edmonton, 2002. 61–70

    Google Scholar 

  27. Cosley D, Huttenlocher D P, Kleinberg J M, et al. Sequential influence models in social networks. In: Proceedings of AAAI ICWSM, Washington, 2010. 26–33

    Google Scholar 

  28. Leskovec J, Krause A, Guestrin C, et al. Cost-effective outbreak detection in networks. In: Proceedings of the 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Jose, 2007. 420–429

    Chapter  Google Scholar 

  29. Watts D J. A simple model of global cascades on random networks. Proc Natl Acad Sci, 2002, 99: 5766–5771

    Article  MATH  MathSciNet  Google Scholar 

  30. Miorandi D, De Pellegrini F. K-Shell decomposition for dynamic complex networks. In: Proceedings of the 8th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt), Avignon, 2010. 488–496

    Google Scholar 

  31. Chen W, Wang Y, Yang S. Efficient influence maximization in social networks. In: Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Paris, 2009. 199–208

    Chapter  Google Scholar 

  32. Jiang Q, Song G, Cong G, et al. Simulated annealing based influence maximization in social networks. In: Proceedings of AAAI, San Francisco, 2011. 127–132

    Google Scholar 

  33. Wang Y, Cong G, Song G, et al. Community based greedy algorithm for mining top-k influential nodes in mobile social networks. In: Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Washington, 2010. 1039–1048

    Chapter  Google Scholar 

  34. Canright G S, Engø Monsen K. Spreading on networks: a topographic view. Complexus, 2006, 3: 131–146

    Article  Google Scholar 

  35. Inoue K, Yokomori R, Yamamoto T, et al. Ranking significance of software components based on use relations. IEEE Trans Softw Eng, 2005, 31: 213–225

    Article  Google Scholar 

  36. Vasa R, Schneider J G, Nierstrasz O. The inevitable stability of software change. In: Proceedings of IEEE International Conference on Software Maintenance, Paris, 2007. 413–422

    Google Scholar 

  37. Martin González A M, Dalsgaard B, Olesen J M. Centrality measures and the importance of generalist species in pollination networks. Ecol Complex, 2010, 7: 36–43

    Article  Google Scholar 

  38. Li C T, Shan M K, Lin S D. Dynamic selection of activation targets to boost the influence spread in social networks. In: Proceedings of the 21st International Conference Companion on World Wide Web, Lyon, 2012. 561–562

    Google Scholar 

  39. Zhang Y, Gu Q, Zheng J, et al. Estimate on expectation for influence maximization in social networks. In: Proceedings of the 14th Pacific-Asia Conference on Advances in Knowledge Discovery and Data Mining, Hyderabad, 2010. 99–106

    Chapter  Google Scholar 

  40. Newman M E J. Power laws, pareto distributions and Zipf’s law. Contemp Phys, 2005, 46: 323–351

    Article  Google Scholar 

  41. Marquardt D W. An algorithm for least-squares estimation of nonlinear parameters. SIAM J Appl Math, 1963, 11: 431–441

    Article  MATH  MathSciNet  Google Scholar 

  42. Mitzenmacher M. A brief history of generative models for power law and lognormal distributions. Internet Math, 2004, 1: 226–251

    Article  MATH  MathSciNet  Google Scholar 

  43. Molloy M, Reed B. A critical point for random graphs with a given degree sequence. Random Struct Algor, 1995, 6: 161–180

    Article  MATH  MathSciNet  Google Scholar 

  44. Myers J L, Well A D. Research Design and Statistical Analysis. Lawrence Erlbaum Associates, 2002

    Google Scholar 

  45. Hall T, Beecham S, Bowes D, et al. A systematic literature review on fault prediction performance in software engineering. IEEE Trans Softw Eng, 2012, 38: 1276–1304

    Article  Google Scholar 

  46. Zhou Y M, Xu B W, Leung H. On the ability of complexity metrics to predict fault-prone classes in object-oriented systems. J Syst Software, 2010, 83: 660–674

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Key Lab of Novel Software Technology and Department of Computer Science and Technology, Nanjing University, Nanjing, 210023, China

    Qing Gu & DaoXu Chen

  2. National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing, 210023, China

    ShiJie Xiong

Authors
  1. Qing Gu
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. ShiJie Xiong
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. DaoXu Chen
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Qing Gu.

Electronic supplementary material

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gu, Q., Xiong, S. & Chen, D. Correlations between characteristics of maximum influence and degree distributions in software networks. Sci. China Inf. Sci. 57, 1–12 (2014). https://doi.org/10.1007/s11432-013-5047-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11432-013-5047-7

Keywords