Takanori Hayashi
Abstract
Measuring the relative importance of each vertex in a network is one of the most fundamental building blocks in network analysis. Among several importance measures, betweenness centrality, in particular, plays key roles in many real applications. Considerable effort has been made for developing algorithms for static settings. However, real networks today are highly dynamic and are evolving rapidly, and scalable dynamic methods that can instantly reflect graph changes into centrality values are required.
In this paper, we present the first fully dynamic method for managing betweenness centrality of all vertices in a large dynamic network. Its main data structure is the weighted hyperedge representation of shortest paths called hypergraph sketch. We carefully design dynamic update procedure with theoretical accuracy guarantee. To accelerate updates, we further propose two auxiliary data structures called two-ball index and special-purpose reachability index. Experimental results using real networks demonstrate its high scalability and efficiency. In particular, it can reflect a graph change in less than a millisecond on average for a large-scale web graph with 106M vertices and 3.7B edges, which is several orders of magnitude larger than the limits of previous dynamic methods.
- T. Akiba, Y. Iwata, and Y. Yoshida. Dynamic and historical shortest-path distance queries on large evolving networks by pruned landmark labeling. In WWW, pages 237--248, 2014. Google Scholar
Digital Library
- J. M. Anthonisse. The Rush In A Directed Graph. Technical Report BN 9/71, Stichting Mathematisch Centrum, 1971.Google Scholar
- D. A. Bader, S. Kintali, K. Madduri, and M. Mihail. Approximating Betweenness Centrality. In WAW, pages 124--137, 2007. Google ScholarDigital Library
- M. Baglioni, F. Geraci, M. Pellegrini, and E. Lastres. Fast Exact Computation of Betweenness Centrality in Social Networks. In ASONAM, pages 450--456, 2012. Google ScholarDigital Library
- A.-L. Barabasi. The origin of bursts and heavy tails in human dynamics. Nature, 435:207--211, 2005.Google ScholarCross Ref
- M. Barthélemy. Betweenness centrality in large complex networks. The European Physical Journal B - Condensed Matter and Complex Systems, 38(2):163--168, 2004.Google Scholar
- E. Bergamini, H. Meyerhenke, and C. L. Staudt. Approximating Betweenness Centrality in Large Evolving Networks. In ALENEX, pages 133--146, 2015. Google ScholarDigital Library
- P. Boldi, M. Rosa, M. Santini, and S. Vigna. Layered Label Propagation: A MultiResolution Coordinate-Free Ordering for Compressing Social Networks. In WWW, 2011. Google ScholarDigital Library
- P. Boldi and S. Vigna. The WebGraph Framework I: Compression Techniques. In WWW, pages 595--601, 2004. Google ScholarDigital Library
- U. Brandes. A Faster Algorithm for Betweenness Centrality. J. Math. Sociol., 25(2):163--177, 2001.Google ScholarCross Ref
- U. Brandes and C. Pich. Centrality Estimation in Large Networks. Int. J. Bifurcat. Chaos, 17(07):2303--2318, 2007.Google ScholarCross Ref
- A. Broder, R. Kumar, F. Maghoul, P. Raghavan, S. Rajagopalan, R. Stata, A. Tomkins, and J. Wiener. Graph Structure in the Web. Comput. Netw., 33(1-6):309--320, 2000. Google ScholarDigital Library
- T. Coffman, S. Greenblatt, and S. Marcus. Graph-based technologies for intelligence analysis. Commun. ACM, 47(3):45--47, 2004. Google ScholarDigital Library
- A. Del Sol, H. Fujihashi, and P. O'Meara. Topology of small-world networks of protein--protein complex structures. Bioinformatics, 21(8):1311--1315, 2005. Google ScholarDigital Library
- D. Erdös, V. Ishakian, A. Bestavros, and E. Terzi. A divide-and-conquer algorithm for betweenness centrality. In SDM, 2015. to appear.Google ScholarCross Ref
- L. C. Freeman. A Set of Measures of Centrality Based on Betweenness. Sociometry, 40(1):35--41, 1977.Google ScholarCross Ref
- D. Frigioni, A. Marchetti-Spaccamela, and U. Nanni. Fully Dynamic Algorithms for Maintaining Shortest Paths Trees. J. Algorithms, 34(2):251--281, 2000. Google ScholarDigital Library
- R. Geisberger, P. Sanders, and D. Schultes. Better Approximation of Betweenness Centrality. In ALENEX, pages 90--100, 2008. Google ScholarDigital Library
- M. Girvan and M. E. J. Newman. Community structure in social and biological networks. P. Natl. Acad. Sci., 99(12):7821--6, 2002.Google ScholarCross Ref
- O. Green, R. McColl, and D. A. Bader. A fast algorithm for streaming betweenness centrality. In SocialCom/PASSAT, pages 11--20, 2012. Google ScholarDigital Library
- H. Jeong, S. P. Mason, A.-L. Barabási, and Z. N. Oltvai. Lethality and centrality in protein networks. Nature, 411(6833):41--42, 2001.Google ScholarCross Ref
- M. Kas, M. Wachs, K. M. Carley, and L. R. Carley. Incremental Algorithm for Updating Betweenness Centrality in Dynamically Growing Networks. In ASONAM, pages 33--40, 2013. Google ScholarDigital Library
- N. Kourtellis, G. D. F. Morales, and F. Bonchi. Scalable Online Betweenness Centrality in Evolving Graphs. Transactions on Knowledge and Data Engineering, 2014. to appear.Google Scholar
- V. E. Krebs. Mapping networks of terrorist cells. Connections, 24(3):43--52, 2002.Google Scholar
- M.-J. Lee, J. Lee, J. Y. Park, R. H. Choi, and C.-W. Chung. QUBE: a Quick algorithm for Updating BEtweenness centrality. In WWW, pages 351--360, 2012. Google ScholarDigital Library
- J. Leskovec and A. Krevl. SNAP Datasets: Stanford large network dataset collection.Google Scholar
- S. Milgram. The Small World Problem. Psychology today, 2(1):60--67, 1967.Google Scholar
- M. E. J. Newman. Networks: An Introduction. Oxford University Press, 2010. Google ScholarDigital Library
- M. E. J. Newman and M. Girvan. Finding and evaluating community structure in networks. Phys. Rev. E, 69:026113, 2004.Google ScholarCross Ref
- R. Puzis, P. Zilberman, Y. Elovici, S. Dolev, and U. Brandes. Heuristics for Speeding Up Betweenness Centrality Computation. In SocialCom/PASSAT, pages 302--311, 2012. Google ScholarDigital Library
- G. Ramalingam and T. W. Reps. On the Computational Complexity of Incremental Algorithms. University of Wisconsin-Madison, Computer Sciences Department, 1991.Google Scholar
- M. Riondato and E. M. Kornaropoulos. Fast Approximation of Betweenness Centrality Through Sampling. In WSDM, pages 413--422, 2014. Google ScholarDigital Library
- K. Tretyakov, A. Armas-cervantes, L. García-ba nuelos, and M. Dumas. Fast Fully Dynamic Landmark-based Estimation of Shortest Path Distances in Very Large Graphs. In CIKM, pages 1785--1794, 2011. Google ScholarDigital Library
- D. J. Watts and S. H. Strogatz. Collective dynamics of 'small-world' networks. Nature, 393(6684):440--442, 1998.Google ScholarCross Ref
- H. Yildirim, V. Chaoji, and M. J. Zaki. DAGGER: A Scalable Index for Reachability Queries in Large Dynamic Graphs. CoRR, abs/1301.0:11, 2013.Google Scholar
- Y. Yoshida. Almost Linear-Time Algorithms for Adaptive Betweenness Centrality using Hypergraph Sketches. In KDD, pages 1416--1425, 2014. Google ScholarDigital Library
- R. Zafarani, M. A. Abbasi, and H. Liu. Social Media Mining: An Introduction. Cambridge University Press, 2014. Google ScholarDigital Library
- A. D. Zhu, W. Lin, S. Wang, and X. Xiao. Reachability Queries on Large Dynamic Graphs: A Total Order Approach. In SIGMOD, pages 1323--1334, 2014. Google ScholarDigital Library
Index Terms
- Fully dynamic betweenness centrality maintenance on massive networks
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