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Randomness Index for complex network analysis

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Abstract

The high-level contribution of this paper is a quantitative measure (called Randomness Index) to assess the extent of randomness in the topology of a complex real-world network. We exploit the observation that the local clustering coefficient (LCC) for a node in a truly random network is independent of the degree of the node and is simply the probability for a link to exist between any two nodes in the network. On the other hand, for real-world networks that are not truly random, nodes with a larger degree are more likely to have a lower LCC value and vice versa. For any complex real-world network, we propose to determine the Randomness Index as the Pearson’s correlation coefficient (ranging from −1 to 1) of the degree versus average LCC of the nodes with the particular degree. We evaluate the Randomness Index values for a suite of 48 real-world networks of diverse degree distribution and observe the median value to be −0.72.

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References

  • Al-Shiridah G, Mahdi K, Safar M (2013) Feedback capacity of different complex network models. In: Proceedings of the 27th international conference on advanced information networking and applications workshops. Barcelona, pp 996–1003

  • Barabasi AL (2016) Network science, 1st edn. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Barabasi AL, Albert R (1999) Emergence of scaling in random networks. Science 286(5439):509–512

    Article  MathSciNet  MATH  Google Scholar 

  • Batagelj V, Mrvar A (2006) Pajek datasets. http://vlado.fmf.uni-lj.si/pub/networks/data/

  • Bernard HR, Killworth PD, Sailer L (1980) Informant accuracy in social network data IV: a comparison of clique-level structure in behavioral and cognitive network data. Soc Netw 2(3):191–218

    Article  Google Scholar 

  • Biedl T, Franz BJ (2001) Graph-drawing contest report. In: Proceedings of the 9th international symposium on graph drawing. pp 513–521

  • Bloznelis M (2013) Degree and clustering coefficient in sparse random intersection graphs. Ann Appl Probab 23(3):1254–1289

    Article  MathSciNet  MATH  Google Scholar 

  • Bonacich P (1987) Power and centrality: a family of measures. Am J Sociol 92(5):1170–1182

    Article  Google Scholar 

  • Britton T, Deijfen M, Martin-Lof A (2006) Generating Simple random graphs with prescribed degree distribution. J Stat Phys 124(6):1377–1397

    Article  MathSciNet  MATH  Google Scholar 

  • Cross RL, Parker A, Cross R (2004) The hidden power of social networks: understanding how work really gets done in organizations, 1st edn. Harvard Business Review Press, Cambridge

    Google Scholar 

  • de Nooy W (1999) A literary playground: literary criticism and balance theory. Poetics 26(5–6):385–404

    Article  Google Scholar 

  • Erdos P, Renyi A (1959) On random graphs I. Publ Math 6:290–297

    MathSciNet  MATH  Google Scholar 

  • Evans JD (1995) Straight forward Statistics for the behavioral sciences, 1st edn. Brooks Cole Publishing Company, Pacific Grove

    Google Scholar 

  • Foudalis I, Jain K, Papadimitriou C, Sideri M (2011) Modeling social networks through user background and behavior. In: Proceedings of the 8th international conference on algorithms and models for the web graph. Atlanta, pp 85–102

  • Freeman LC, Freeman SC, Michaelson AG (1989) How humans see social groups: a test of the Sailer–Gaulin models. J Quant Anthropol 1:229–238

    Google Scholar 

  • Freeman LC, Webster CM, Kirke DM (1998) Exploring social structure using dynamic three-dimensional color images. Soc Netw 20(2):109–118

    Article  Google Scholar 

  • Geiser P, Danon L (2003) Community structure in jazz. Adv Complex Syst 6(4):563–573

    Google Scholar 

  • Gemmetto V, Barrat A, Cattuto C (2014) Mitigation of infectious disease at school: targeted class closure vs. school closure. BMC Infect Dis 14(695):1–10

    Google Scholar 

  • Gil-Mendieta J, Schmidt S (1996) The political network in Mexico. Soc Netw 18(4):355–381

    Article  Google Scholar 

  • Girvan M, Newman MEJ (2002) Community structure in social and biological networks. Proc Natl Acad Sci USA 99(12):7821–7826

    Article  MathSciNet  MATH  Google Scholar 

  • Gleiser PM (2007) How to become a superhero. J Stat Mech Theory Exp 2007:P09020

    Article  Google Scholar 

  • Godehardt E, Jaworski J (2001) Two models of random intersection graphs and their applications. Electron Notes Discrete Math 104:129–132

    Article  MATH  Google Scholar 

  • Grimmer J (2010) A Bayesian hierarchical topic mode for political texts: measuring expressed agendas in Senate press releases. Political Anal 18(1):1–35

    Article  Google Scholar 

  • Hayes B (2006) Connecting the dots. Am Sci 94(5):400–404

    Article  Google Scholar 

  • Hummon NP, Doreian P, Freeman LC (1990) Analyzing the structure of the centrality-productivity literature created between 1948 and 1979. Sci Commun 11(4):459–480. doi:10.1177/107554709001100405

    Google Scholar 

  • Humphries MD, Gurney K (2008) Network ‘small-world-ness’: a quantitative method for determining canonical network equivalence. PLoS ONE 3(4):e0002051

    Article  Google Scholar 

  • Isella L, Stehle J, Barrat A, Cattuto C, Pinton JF, Van den Broeck W (2011) What’s in a crowd? Analysis of face-to-face behavioral networks. J Theor Biol 271(1):166–180. doi:10.1016/j.jtbi.2010.11.033

    Article  MathSciNet  Google Scholar 

  • Knuth DE (1993) The Stanford GraphBase: a platform for combinatorial computing, 1st edn. Addison-Wesley, Reading

    MATH  Google Scholar 

  • Krackhardt D (1999) The ties that torture: Simmelian tie analysis in organizations. Res Sociol Organ 16:183–210

    Google Scholar 

  • Krebs V (2003) Proxy networks: analyzing One network to reveal another. Bull Méthodol Sociol 79:61–70

    Article  Google Scholar 

  • Lee J-S (2004) Generating networks of illegal drug users using large samples of partial ego-network data. In: Intelligence and security informatics (Lecture nodes in computer science), vol 3073. pp 390–402

  • Li M, O’Riordan C (2013) The Effect of clustering coefficient and node degree on the robustness of cooperation. In: Proceedings of the 2013 IEEE congress on evolutionary computation. Cancun, pp 2833–2839

  • Loomis CP, Morales JO, Clifford RA, Leonard OE (1953) Turrialba social systems and the introduction of change. The Free Press, Glencoe, pp 45–78

    Google Scholar 

  • Lusseau D, Schneider K, Boisseau OJ, Haase P, Slooten E, Dawson SM (2003) The bottlenose dolphin community of Doubtful Sound features a large proportion of long-lasting associations. Behav Ecol Sociobiol 54(3):396–405

    Article  Google Scholar 

  • MacRae D (1960) Direct factor analysis of sociometric data. Sociometry 23(4):360–371

    Article  MathSciNet  Google Scholar 

  • C. McCarty and L. Freeman, http://moreno.ss.uci.edu/data.html, 2008

  • Meghanathan N (2014) Spectral radius as a measure of variation in node degree for complex network graphs. In: Proceedings of the 3rd international conference on digital contents and applications. Hainan, pp 30–33

  • Meghanathan N (2015) Distribution of maximal clique size of the vertices for theoretical small-world networks and real-world networks. Int J Comput Netw Commun 7(4):21–41

    Google Scholar 

  • Meghanathan N (2016) On the sufficiency of using the degree sequence of the vertices to generate random networks corresponding to real-world networks. Polibits Res J Comput Sci Comput Eng Appl 53:5–21

    Google Scholar 

  • Meghanathan N (2017a) A computationally-lightweight and localized centrality metric in lieu of betweenness centrality for complex network analysis. Springer Vietnam J Comput Sci 4(1):23–38

    Article  Google Scholar 

  • Meghanathan N (2017b) Complex network analysis of the contiguous United States graph. Comput Inf Sci 10(1):54–76

    Google Scholar 

  • Michael JH (1997) Labor dispute reconciliation in a forest products manufacturing facility. For Prod J 47(11–12):41–45

    Google Scholar 

  • Moreno JL (1960) The sociometry reader. The Free Press, Glencoe, pp 534–547

    Google Scholar 

  • Nepusz T, Petroczi A, Negyessy L, Bazso F (2008) Fuzzy communities and the concept of bridgeness in complex networks. Phys Rev E 77(1):016107

    Article  MathSciNet  Google Scholar 

  • Newman MEJ (2002) Assortative mixing in networks. Phys Rev Lett 89(20):208701

    Article  Google Scholar 

  • Newman MEJ (2010) Networks: an introduction, 1st edn. Oxford University Press, Oxford

    Book  MATH  Google Scholar 

  • Newman MEJ (2006) Finding community structure in networks using the eigenvectors of matrices. Phys Rev E 74(3):036104

    Article  MathSciNet  Google Scholar 

  • Pearson M, Michell L (2000) Smoke rings: social network analysis of friendship groups, smoking and drug-taking. Drugs Educ Prev Policy 7(1):21–37

    Article  Google Scholar 

  • Pizzuti C, Rombo SE (2014) Algorithms and tools for protein-protein interaction networks clustering, with a special focus on population-based stochastic methods. Bioinformatics 30(10):1343–1352

    Article  Google Scholar 

  • Ravasz L, Barabasi AL (2003) Hierarchical organization in complex networks. Phys Rev E 67:026112

    Article  MATH  Google Scholar 

  • Resnick MD, Bearman PS, Blum RW, Bauman KE, Harris KM, Jones J, Tabor J, Beuhring T, Sieving RE, Shew M, Ireland M, Bearinger LH, Udry JR (1997) Protecting adolescents from harm. Findings from the National Longitudinal Study on Adolescent Health. J Am Med Assoc 278(10):823–832

    Article  Google Scholar 

  • Rogers EM, Kincaid DL (1980) Communication networks: toward a new paradigm for research. Free Press, New York

    Google Scholar 

  • Schwimmer E (1973) Exchange in the social structure of the Orokaiva: traditional and emergent ideologies in the Northern District of Papua. C Hurst and Co-Publishers Ltd., London

    Google Scholar 

  • Scott JP (1980) The anatomy of Scottish capital: Scottish companies and Scottish capital, 1st edn. Brooks Cole Publishing Company, Pacific Grove, pp 1900–1979

    Book  Google Scholar 

  • Smith DA, White DR (1992) Structure and dynamics of the global economy: network Analysis of international trade 1965–1980. Soc Forces 70(4):857–893

    Article  Google Scholar 

  • Soffer SN, Vazquez A (2005) Clustering coefficient without degree correlations biases. Phys Rev 7:057101

    Google Scholar 

  • Strang G (2006) Linear algebra and its applications, 4th edn. Brooks Cole, Pacific Grove

    MATH  Google Scholar 

  • Takahata Y (1991) Diachronic changes in the dominance relations of adult female Japanese monkeys of the Arashiyama B group. In: Fedigan LM, Asquith PJ (eds) The monkeys of Arashiyama. State University of New York Press, Albany, pp 124–139

    Google Scholar 

  • Ugarte MD, Militino AF, Arnholt AT (2015) Probability and statistics with R, 2nd edn. Chapman and Hall, Boca Raton

    MATH  Google Scholar 

  • Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393:440–442

    Article  MATH  Google Scholar 

  • White JG, Southgate E, Thomson JN, Brenner S (1986) The structure of the nervous system of the nematode Caenorhabditis elegans. Philos Trans B 314(1165):1–340

    Article  Google Scholar 

  • Zachary WW (1977) An information flow model for conflict and fission in small groups. J Anthropol Res 33(4):452–473

    Article  Google Scholar 

Download references

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  1. Jackson State University, Jackson, MS, 39217, USA

    Natarajan Meghanathan

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Meghanathan, N. Randomness Index for complex network analysis. Soc. Netw. Anal. Min. 7, 25 (2017). https://doi.org/10.1007/s13278-017-0444-3

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  • DOI: https://doi.org/10.1007/s13278-017-0444-3

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