The notions of betweenness centrality (BC) and group betweenness centrality (GBC) are widely used in social network analyses. We introduce variants of them; namely, the k-step BC and k-step GBC. The k-step GBC of a group of vertices in a network is a measure of the likelihood that at least one group member will get the information communicated between pairs of vertices through shortest paths within the first k steps of the start of the communication. The k-step GBC of a single vertex is the k-step BC of that vertex. The introduced centrality measures may find uses in applications where it is important or critical to obtain the information within a fixed time of the start of the communication. For the introduced centrality measures, we propose an algorithm that can compute successively the k-step GBC of several groups of vertices. The performance of the proposed algorithm is evaluated through computational experiments. The use of the new BC measures leads to an earlier control of the information (virus, malware, or rumor) before it spreads through the network.
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Barabási AL, Albert R (1999) Emergence of scaling in random networks. Science 286(5439):509–512. https://doi.org/10.1126/science.286.5439.509
Borgatti S, Everett M (2006) A graph-theoretic perspective on centrality. Soc Netw 28:466–484. https://doi.org/10.1016/j.socnet.2005.11.005
Brandes U (2001) A faster algorithm for betweenness centrality. J Math Sociol 25(2):163–177. https://doi.org/10.1080/0022250X.2001.9990249
Brandes U (2008) On variants of shortest-path betweenness centrality and their generic computation. Soc Netw 30(2):136–145. https://doi.org/10.1016/j.socnet.2007.11.001
Chen W, Lu W, Zhang N (2012) Time-critical influence maximization in social networks with time-delayed diffusion process. In: Proceedings of the twenty-sixth AAAI conference on artificial intelligence, AAAI Press, AAAI’12, pp 592–598
Colladon AF, Guardabascio B, Innarella R (2019) Using social network and semantic analysis to analyze online travel forums and forecast tourism demand. Decis Support Syst 123:113075. https://doi.org/10.1016/j.dss.2019.113075
Das K, Samanta S, Pal M (2018) Study on centrality measures in social networks: a survey. Soc Netw Anal Min 8(1):13. https://doi.org/10.1007/s13278-018-0493-2
Dolev S, Elovici Y, Puzis R, Zilberman P (2009) Incremental deployment of network monitors based on group betweenness centrality. Inf Process Lett 109(20):1172–1176. https://doi.org/10.1016/j.ipl.2009.07.019
Everett MG, Borgatti SP (1999) The centrality of groups and classes. J Math Sociol 23(3):181–201. https://doi.org/10.1080/0022250X.1999.9990219
Freeman LC (1977) A set of measures of centrality based on betweenness. Sociometry 40(1):35–41. https://doi.org/10.2307/3033543
Freeman LC (1978–1979) Centrality in social networks conceptual clarification. Soc Netw 1(3):215–239. https://doi.org/10.1016/0378-8733(78)90021-7
Grassi R, Calderoni F, Bianchi M, Torriero A (2019) Betweenness to assess leaders in criminal networks: new evidence using the dual projection approach. Soc Netw 56:23–32. https://doi.org/10.1016/j.socnet.2018.08.001
Guan J, Yan Z, Yao S, Xu C, Zhang H (2017) GBC-based caching function group selection algorithm for SINET. J Netw Comput Appl 85:56–63. https://doi.org/10.1016/j.jnca.2016.12.004
Hayashi T, Akiba T, Yoshida Y (2015) Fully dynamic betweenness centrality maintenance on massive networks. Proc VLDB Endow 9(2):48–59. https://doi.org/10.14778/2850578.2850580
Kchiche A, Kamoun F (2009) Access-points deployment for vehicular networks based on group centrality. In: Proceedings of the 2009 3rd international conference on new technologies, mobility and security pp 1–6. https://doi.org/10.1109/NTMS.2009.5384770
Kolaczyk ED, Chua DB, Barthélemy M (2009) Group betweenness and co-betweenness: inter-related notions of coalition centrality. Soc Netw 31(3):190–203. https://doi.org/10.1016/j.socnet.2009.02.003
Lee MJ, Choi S, Chung CW (2016) Efficient algorithms for updating betweenness centrality in fully dynamic graphs. Inform Sci 326:278–296. https://doi.org/10.1016/j.ins.2015.07.053
Leskovec J, Krevl A (2014) SNAP Datasets: Stanford large network dataset collection. http://snap.stanford.edu/data, Accessed 27 Feb 2019
Liu B, Cong G, Xu D, Zeng Y (2012) Time constrained influence maximization in social networks. In: Proceedings of the 2012 IEEE 12th international conference on data mining, pp 439–448. https://doi.org/10.1109/ICDM.2012.158
Lujak M, Giordani S (2018) Centrality measures for evacuation: finding agile evacuation routes. Future Gener Comput Syst 83:401–412. https://doi.org/10.1016/j.future.2017.05.014
Newman JM (2003) A measure of betweenness centrality based on random walks. Soc Netw 27:39–54. https://doi.org/10.1016/j.socnet.2004.11.009
Ni C, Sugimoto CR, Jian J (2011) Degree, closeness, and betweenness: application of group centrality measurements to explore macro-disciplinary evolution diachronically. In: Proceedings of the 13th international society of scientometrics and informetrics conference (ISSI), pp 1–13
Puzis R, Elovici Y, Dolev S (2007a) Fast algorithm for successive computation of group betweenness centrality. Phys Rev E 76:056709. https://doi.org/10.1103/PhysRevE.76.056709
Puzis R, Elovici Y, Dolev S (2007b) Finding the most prominent group in complex networks. AI Commun 20(4):287–296
Puzis R, Tubi M, Elovici Y, Glezer C, Dolev S (2011) A decision support system for placement of intrusion detection and prevention devices in large-scale networks. ACM Trans Model Comput Simul 22:5. https://doi.org/10.1145/2043635.2043640
Puzis R, Altshuler Y, Elovici Y, Bekhor S, Shiftan Y, Pentland AS (2013) Augmented betweenness centrality for environmentally aware traffic monitoring in transportation networks. J Intell Transp Syst 17(1):91–105. https://doi.org/10.1080/15472450.2012.716663
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, Accessed 27 Feb 2019
Rysz M, Pajouh FM, Pasiliao EL (2018) Finding clique clusters with the highest betweenness centrality. Eur J Oper Res 271(1):155–164. https://doi.org/10.1016/j.ejor.2018.05.006
Szczepański PL, Michalak TP, Rahwan T (2016) Efficient algorithms for game-theoretic betweenness centrality. Artif Intell 231:39–63. https://doi.org/10.1016/j.artint.2015.11.001
Tubi M, Puzi R, Elovici Y (2007) Deployment of DNIDS in social networks. In: 2007 IEEE intelligence and security informatics, pp 59–65. https://doi.org/10.1109/ISI.2007.379534
Veremyev A, Prokopyev OA, Pasiliao EL (2017) Finding groups with maximum betweenness centrality. Optim Methods Softw 32(2):369–399. https://doi.org/10.1080/10556788.2016.1167892
Willoughby R (1970) The University of Florida sparse matrix collection. https://sparse.tamu.edu, Accessed 27 Feb 2019
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Akgün, M.K., Tural, M.K. k-step betweenness centrality. Comput Math Organ Theory 26, 55–87 (2020). https://doi.org/10.1007/s10588-019-09301-9
- Group betweenness
- Network analysis
- Social networks
- k-step betweenness