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An incremental algorithm for updating betweenness centrality and k-betweenness centrality and its performance on realistic dynamic social network data

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The increasing availability of dynamically changing digital data that can be used for extracting social networks over time has led to an upsurge of interest in the analysis of dynamic social networks. One key aspect of dynamic social network analysis is finding the central nodes in a network. However, dynamic calculation of centrality values for rapidly changing networks can be computationally expensive, with the result that data are frequently aggregated over many time periods and only intermittently analyzed for centrality measures. This paper presents an incremental betweenness centrality algorithm that efficiently updates betweenness centralities or k-betweenness centralities of nodes in dynamic social networks by avoiding re-computations through the efficient storage of information from earlier computations. In this paper, we evaluate the performance of the proposed algorithms for incremental betweenness centrality and k-betweenness centrality on both synthetic social network data sets and on several real-world social network data sets. The presented incremental algorithm can achieve substantial performance speedup (3–4 orders of magnitude faster for some data sets) when compared to the state of the art. And, incremental k-betweenness centrality, which is a good predictor of betweenness centrality, can be carried out on social network data sets with millions of nodes.

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  • Bader D, Madduri K (2006) Parallel algorithms for evaluating centrality indices in real-world networks. International conference on parallel processing (ICPP). IEEE, pp 539–550

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

    Article  MathSciNet  Google Scholar 

  • Batagelj V, Kejžar N, Korenjak-Černe S, Zaveršnik M (2006). Analyzing the structure of US patents network. Springer, Berlin

  • Berman AM (1992) Lower and upper bounds for incremental algorithms. Ph.D. Dissertation, The State University of New Jersey at Rutgers, Computer Science, New Brunswick

  • Borgatti SP, Everett MG (2006) A graph-theoretic perspective on centrality. Soc Netw 28(4):466–484

    Article  Google Scholar 

  • Brandes U (2001) A faster algorithm for betweenness centrality. J Math Sociol 25(2):163–177

    Article  MATH  Google Scholar 

  • Brandes U (2008) On variants of shortest-path betweenness centrality and their generic computation. Soc Netw 30(2):136–145

    Article  MathSciNet  Google Scholar 

  • Demetrescu C, Italiano GF (2004) A new approach to dynamic all pairs shortest paths. J ACM (JACM) 51(6):968–992

    Article  MathSciNet  MATH  Google Scholar 

  • Demetrescu C, Italiano GF (2006) Experimental analysis of dynamic all pairs shortest path algorithms. ACM Trans Algorithms (TALG) 2(4):578–601

    Article  MathSciNet  Google Scholar 

  • Dijkstra E (1959) A note on two problems in connexion with graphs. Numer Math 1(1):269–271

    Article  MathSciNet  MATH  Google Scholar 

  • Even S, Gazit H (1985) Updating distances in dynamic graphs. Methods Oper Res 49:371–387

    MathSciNet  MATH  Google Scholar 

  • Floyd R (1962) Algorithm 97: shortest path. Commun ACM 5(6):345

    Article  Google Scholar 

  • Fredman ML, Tarjan RE (1984). Fibonacci heaps and their uses in improved network optimization algorithms. 25th annual symposium on foundations of computer science. IEEE, pp 338–346

  • Freeman LC (1977) A set of measures of centrality based on betweenness. Sociometry 40(1):35–41

    Article  Google Scholar 

  • GraphStream Team (2010) GraphStream. Retrieved 3 February 2012.

  • Green O, McColl R, Bader DA (2012). A fast algorithm for streaming betweenness centrality. International Conference on Privacy, Security, Risk and Trust (PASSAT) and International Conference on Social Computing (SocialCom). IEEE, Amsterdam, pp 11–20

  • Gringoli FE (2009) GT: picking up the truth from the ground for internet traffic. Comput Commun Rev 39(5):13–18

    Article  Google Scholar 

  • Habiba H, Tantipathananandh C, Berger-Wolf T (2007) Betweenness centrality measure in dynamic networks. University of Illinois at Chicago, Department of Computer Science. DIMACS, Chicago

  • Isella LE (2011) What’s in a crowd? Analysis of face-to-face behavioral networks. J Theor Biol 271(1):166–180

    Article  MathSciNet  Google Scholar 

  • Jiang K, Ediger D, Bader DA (2009) Generalizing k-betweenness centrality using short paths and a parallel multithreaded implementation. International conference on parallel processing (ICPP), Vienna, pp 542–549

  • Kas M (2013b) Incremental centrality algorithms for dynamic network analysis. Ph.D. Dissertation, Carnegie Mellon University, ECE, Pittsburgh

  • Kas M, Wachs M, Carley L, Carley K (2012a). Incremental centrality computations for dynamic social networks. XXXII international sunbelt social network conference (Sunbelt 2012). INSNA, Redondo Beach

  • Kas M, Carley KM, Carley LR (2012b) Trends in science networks: understanding structures and statistics of scientific networks. Social network analysis and mining (SNAM)

  • Kas M, Wachs M, Carley K, Carley L (2013) incremental algorithm for updating betweenness centrality in dynamically growing networks. The 2013 IEEE/ACM international conference on advances in social networks analysis and mining (ASONAM). IEEE, Niagara Falls

  • Kim H, Anderson R (2012) Temporal node centrality in complex networks. Phys Rev E 85(026107):1–8

    MATH  Google Scholar 

  • King, V. (1999). Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs. 40th annual symposium on foundations of computer science. IEEE, pp 81–89

  • Kourtellis N, Alahakoon T, Simha R, Iamnitchi A, Tripathi R (2013) Identifying high betweenness centrality nodes in large social networks. Soc Netw Anal Min (SNAM) 4(3):899–914

    Article  Google Scholar 

  • Lee MJ, Lee J, Park JY, Choi R, Chung CW (2012a) QUBE: a Quick algorithm for updating BEtweenness centrality. WWW, ACM, pp 351–360

  • Lee MJ, Lee J, Park JY, Choi R, Chung CW (2012b) QUBE: a quick algorithm for updating BEtweenness centrality. In: Proceedings of the 21st international conference on World Wide Web (WWW). ACM, Lyon, pp 351–360

  • Lerman K, Ghosh R, Kang JH (2010) Centrality metric for dynamic networks. 8th workshop on mining and learning with graphs (MLG). ACM, pp 70–77

  • Leskovec J, Kleinberg J, Faloutsos C (2007) Graph evolution: densification and shrinking diameters. ACM Trans KDD 1(2):1–41

    Google Scholar 

  • Leskovec J, Huttenlocher DP, Kleinberg JM (2010) Governance in social media: a case study of the Wikipedia promotion process. The international AAAI conference on weblogs and social media (ICWSM)

  • Liao W, Ding J, Marinazzo D, Xu Q, Wang Z, Yuan C et al (2011) Small-world directed networks in the human brain: multivariate Granger causality analysis of resting-state fMRI. Neuroimage 54(4):2683–2694

    Article  Google Scholar 

  • Norlen K, Lucas G, Gebbie M, Chuang J (2002) EVA: extraction, visualization and analysis of the telecommunications and media ownership network. International telecommunications society 14th biennial conference

  • Onnela JP, Saramäki J, Hyvönen J, Szabó G, Lazer D, Kaski K et al (2007) Structure and tie strengths in mobile communication networks. Proc Natl Acad Sci 104(18):7332–7336

    Article  Google Scholar 

  • Opsahl T, Panzarasa P (2009) Clustering in weighted networks. Soc Netw 31(2):155–163

    Article  Google Scholar 

  • Pfeffer J, Carley KM (2012) k-Centralities: local approximations of global measures based on shortest paths. WWW. ACM, pp 1043–1050

  • Puzis R, Zilberman P, Elovici Y, Dolev S, Brandes U (2012) Heuristics for speeding up betweenness centrality computation. Social computing and on privacy, security, risk and trust. IEEE Computer Society, pp 302–311

  • Ramalingam G, Reps T (1991a) On the computational complexity of incremental algorithms. Technical report, University of Wisconsin at Madison

  • Ramalingam G, Reps T (1991b) On the computational complexity of incremental algorithms. Technical Report, University of Wisconsin at Madison, Computer Science, Madison

  • Ramezanpour A, Karimipour V (2008) Simple models of small world networks with directed links. Sharif University of Technology, Department of Physics, Tehran

  • Renyi A, Erdos P (1959). On random graphs. Publicationes Mathematicae, 6

  • Tang J, Musolesi M, Mascolo C, Latora V, Nicosia V (2010) Analysing information flows and key mediators through temporal centrality metrics. 3rd workshop on social network systems (SNS). April

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

  • Xu J (2008) Markov chain small world model with asymmetric transition probabilities. Electron J Linear Algebra 17:616–636

    MathSciNet  MATH  Google Scholar 

  • Yang J, Leskovec J (2011). Patterns of temporal variation in online media. International conference on web search and data minig (WSDM). ACM

  • Zhu C, Xiong S, Tian Y, Li N, Jiang K (2004). Scaling of directed dynamical small-world networks with random responses. Phys Rev Lett 92 218702(24):1–4

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This work is supported in part by the Defense Threat Reduction Agency (HDTRA11010102), and by the center for Computational Analysis of Social and Organizational Systems (CASOS) at Carnegie Mellon. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied by the DTRA or the US government. This work is done when Miray Kas was a Ph.D. student in Carnegie Mellon University’s Electrical and Computer Engineering department.

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Correspondence to L. Richard Carley.

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This paper was invited as an extended version of Miray Kas, Matthew Wachs, Kathleen M. Carley, L. Richard Carley. Incremental Algorithm for Updating Betweenness Centrality in Dynamically Growing Networks. The 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM), August 25–28, 2013, Niagara Falls, Canada.



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Kas, M., Carley, K.M. & Carley, L.R. An incremental algorithm for updating betweenness centrality and k-betweenness centrality and its performance on realistic dynamic social network data. Soc. Netw. Anal. Min. 4, 235 (2014).

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