Abstract
Social networks have demonstrated in the last few years to be a powerful and flexible concept useful to represent and analyze data emerging from social interactions and social activities. The study of these networks can thus provide a deeper understanding of many emergent global phenomena. The amount of data available in the form of social networks is growing by the day. This poses many computational challenging problems for their analysis. In fact many analysis tools suitable to analyze small to medium sized networks are inefficient for large social networks. The computation of the betweenness centrality index (BC) is a well established method for network data analysis and it is also important as subroutine in more advanced algorithms, such as the Girvan-Newman method for graph partitioning. In this chapter we present a novel approach for the computation of the betweenness centrality, which speeds up considerably Brandes’ algorithm (the current state of the art) in the context of social networks. Our approach exploits the natural sparsity of the data to algebraically (and efficiently) determine the betweenness of those nodes forming trees (tree-nodes) in the social network. Moreover, for the residual network, which is often of much smaller size, we modify directly the Brandes’ algorithm so that we can remove the nodes already processed and perform the computation of the shortest paths only for the residual nodes. We also give a fast sampling-based algorithm that computes an approximation of the betweenness centrality values of the residual network while returns the exact value for the tree-nodes. This algorithm improves in speed and precision over current state of the art approximation methods. Tests conducted on a sample of publicly available large networks from the Stanford repository show that, for the exact algorithm, speed improvements of a factor ranging between 2 and 5 are possible on several such graphs, when the sparsity, measured by the ratio of tree-nodes to the total number of nodes, is in a medium range (30–50 %). For some large networks from the Stanford repository and for a sample of social networks provided by Sistemi Territoriali with high sparsity (80 % and above) tests show that our algorithm, named SPVB (for Shortest Path Vertex Betweenness), consistently runs between one and two orders of magnitude faster than the current state of the art exact algorithm.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
- 2.
For nodes whose BC exact value is zero, the partial BC contribution for any source is also zero, thus the sampling procedure will estimate the correct value, zero.
References
Koschatzki D, Lehmann K, Peeters L, Richter S, Tenfelde-Podehl D, Zlotowski O (2005) Centrality indices. In: Brandes U, Erlebach T (eds) Network analysis. Lecture notes in computer science, vol 3418. Springer, Berlin, pp 16–61
Borgatti SP (2005) Centrality and network flow. Social Netw 27(1):55–71
Anthonisse JM (1971) The rush in a directed graph. Technical Report BN 9/71, Stichting Mathematisch Centrum, 2e Boerhaavestraat 49 Amsterdam
Freeman LC (1977) A set of measures of centrality based on betweenness. Sociometry 40(1):35–41
Del Sol A, Fujihashi H, O’Meara P (2005) Topology of small-world networks of protein–protein complex structures. Bioinformatics 21:1311–1315
Leydesdorff L (2007) Betweenness centrality as an indicator of the interdisciplinarity of scientific journals. J Am Soc Inf Sci Technol 58:1303–1309
Girvan M, Newman MEJ (2002) Community structure in social and biological networks. Proc Natl Acad Sci USA 99:7821–7826
Brandes U (2008) On variants of shortest-path betweenness centrality and their generic computation. Social Netw 30(2):136–145
Brandes Ulrik (2001) A faster algorithm for betweenness centrality. J Math Sociol 25(2):163–177
Bader D, Kintali S, Madduri K, Mihail M (2007) Approximating betweenness centrality. In: Bonato A, Chung F (eds) Algorithms and models for the Web-Graph, vol 4863. Lecture Notes in Computer Science. Springer, Berlin, pp 124–137
Jacob R, Dirk K, Lehmann K, Peeters L, Tenfelde-Podehl D (2005) Algorithms for centrality indices. In: Brandes U, Erlebach T (eds) Network analysis. Lecture notes in computer science, vol 3418. Springer, Berlin/Heidelberg, pp 62–82
Bader DA, Madduri K (2006) Parallel algorithms for evaluating centrality indices in real-world networks. In: International conference on parallel processing, 2006, ICPP 2006, pp 539–550
Kintali S (2008) Betweenness centrality: algorithms and lower bounds. CoRR, abs/0809.1906
Madduri K, Ediger D, Jiang K, Bader DA, Chavarria-Miranda D (2009) A faster parallel algorithm and efficient multithreaded implementations for evaluating betweenness centrality on massive datasets. Parallel and distributed processing symposium, international, pp 1–8
Brandes U, Pich C (2007) Centrality estimation in large networks. I J Bifurcat Chaos 17(7):2303–2318
Geisberger R, Sanders P, Schultes D (2008) Better approximation of betweenness centrality. In: ALENEX, pp 90–100
White S, Smyth P (2003) Algorithms for estimating relative importance in networks. In: Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining, KDD ’03, ACM, New York, pp 266–275
Everett M, Borgatti SP (2005) Ego network betweenness. Social Netw 27(1):31–38
Carpenter T, Karakosta G, Shallcross D (2002) Practical issues and algorithms for analyzing terrorist networks, 2002. Invited paper at WMC 2002
Newman MEJ (2005) A measure of betweenness centrality based on random walks. Social Netw 27(1):39–54
Chan SY, Leung IXY, Liò P (2009) Fast centrality approximation in modular networks. In: CIKM-CNIKM, pp 31–38
Green O, McColl R, Bader DA (2012) Fast algorithm for incremental betweenness centrality. In: Proceeding of SE/IEEE international conference on social computing (SocialCom), 3–5 Sept 2012
Lee M-J, Lee J, Park JY, Choi RH, Chung C-W (2012) QUBE: a quick algorithm for updating betweenness centrality. In: Proceedings of the 21st international conference on World Wide Web, WWW ’12, ACM, New York, pp 351–360
Puzis R, Zilberman P, Elovici Y, Dolev S, Brandes U (2012) Heuristics for speeding up betweenness centrality computation. In: Proceeding of SE/IEEE international conference on social computing (SocialCom), 3–5 Sept 2012
Baglioni M, Geraci F, Pellegrini M, Lastres E (2012) Fast exact computation of betweenness centrality in social networks. In: Proceedings of the 2012 IEEE/ACM international conference on advances in social networks analysis and mining (ASONAM 2012), Istambul, Turkey, 26–29 Aug 2012
Acknowledgments
This research is partially supported by the project BINet “Nuova Piattaforma di Business Intelligence Basata sulle Reti Sociali" funded by Regione Toscana POR CReO 2007–2013 Programme.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Baglioni, M., Geraci, F., Pellegrini, M., Lastres, E. (2014). Fast Exact and Approximate Computation of Betweenness Centrality in Social Networks. In: Can, F., Özyer, T., Polat, F. (eds) State of the Art Applications of Social Network Analysis. Lecture Notes in Social Networks. Springer, Cham. https://doi.org/10.1007/978-3-319-05912-9_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-05912-9_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05911-2
Online ISBN: 978-3-319-05912-9
eBook Packages: Computer ScienceComputer Science (R0)