Finding patterns in the degree distribution of real-world complex networks: going beyond power law
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The most important structural characteristics in the study of large-scale real-world complex networks in pattern analysis are degree distribution. Empirical observations on the pattern of the real-world networks have led to the claim that their degree distributions follow, in general, a single power law. However, a closer observation, while fitting, shows that the single power-law distribution is often inadequate to meet the data characteristics properly. Since the degree distribution in the log–log scale actually displays, under inspection, two different slopes unlike what happens while fitting with the single power law. These two slopes with a transition in between closely resemble the pattern of the sigmoid function. This motivates us to derive a novel double power-law distribution for accurately modeling the real-world networks based on the sigmoid function. The proposed modeling approach further leads to the identification of a transition degree which, it has been demonstrated, may have a significant implication in analyzing the complex networks. The applicability, as well as effectiveness of the proposed methodology, is shown using rigorous experiments and also validated using statistical tests.
KeywordsDegree distribution Power-law distribution Sigmoid function Hyperbolic tangent function KL-divergence Goodness-of-fit
The authors gratefully acknowledge the financial assistance received from Indian Statistical Institute (I. S. I.) and Visvesvaraya PhD Scheme awarded by the Government of India.
- 9.Bollobás B, Riordan OM (2003) Mathematical results on scale-free random graphs. In: Bornholdt S, Schuster HG (eds) Handbook of graphs and networks: from the genome to the internet. Wiley, London, pp 1–34Google Scholar
- 19.Kleinberg JM, Kumar R, Raghavan P, Rajagopalan S, Tomkins AS (1999) The web as a graph: measurements, models, and methods. In: International computing and combinatorics conference. Springer, pp 1–17Google Scholar
- 20.Leskovec J, Krevl A (2014) SNAP Datasets: Stanford large network dataset collection. http://snap.stanford.edu/data
- 30.Rossi RA, Ahmed NK (2015) The network data repository with interactive graph analytics and visualization. In: Proceedings of the twenty-ninth AAAI conference on artificial intelligence. http://networkrepository.com
- 31.Sala A, Zheng H, Zhao BY, Gaito S, Rossi GP (2010) Brief announcement: revisiting the power-law degree distribution for social graph analysis. In: Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing. ACM, pp 400–401Google Scholar
- 33.Seshadri M, Machiraju S, Sridharan A, Bolot J, Faloutsos C, Leskove J (2008) Mobile call graphs: beyond power-law and lognormal distributions. In: Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, pp 596–604Google Scholar
- 34.Song Y, Zhang C, Wu M (2010) The study of human behavior dynamics based on blogosphere. In: 2010 International conference on web information systems and mining (WISM), vol 1. IEEE, pp 87–91Google Scholar