Lutz Oettershagen
ABSTRACT
We propose the Temporal Walk Centrality, which quantifies the importance of a node by measuring its ability to obtain and distribute information in a temporal network. In contrast to the widely-used betweenness centrality, we assume that information does not necessarily spread on shortest paths but on temporal random walks that satisfy the time constraints of the network. We show that temporal walk centrality can identify nodes playing central roles in dissemination processes that might not be detected by related betweenness concepts and other common static and temporal centrality measures. We propose exact and approximation algorithms with different running times depending on the properties of the temporal network and parameters of our new centrality measure. A technical contribution is a general approach to lift existing algebraic methods for counting walks in static networks to temporal networks. Our experiments on real-world temporal networks show the efficiency and accuracy of our algorithms. Finally, we demonstrate that the rankings by temporal walk centrality often differ significantly from those of other state-of-the-art temporal centralities.
- Josh Alman and Virginia Vassilevska Williams. 2021. A Refined Laser Method and Faster Matrix Multiplication. In Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms, SODA, Dániel Marx (Ed.). SIAM, 522–539.Google Scholar
Cross Ref
- Ferenc Béres, Róbert Pálovics, Anna Oláh, and András A. Benczúr. 2018. Temporal walk based centrality metric for graph streams. Applied Network Science 3, 1 (2018), 32:1–32:26.Google Scholar
- Ulrik Brandes. 2001. A faster algorithm for betweenness centrality. The Journal of Mathematical Sociology 25, 2 (2001), 163–177.Google ScholarCross Ref
- Sergey Brin and Lawrence Page. 1998. The anatomy of a large-scale hypertextual web search engine. Computer networks and ISDN systems 30, 1-7 (1998), 107–117.Google Scholar
- Sebastian Buß, Hendrik Molter, Rolf Niedermeier, and Maciej Rymar. 2020. Algorithmic Aspects of Temporal Betweenness. In KDD ’20: The 26th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. ACM, 2084–2092.Google ScholarDigital Library
- Don Coppersmith and Shmuel Winograd. 1987. Matrix multiplication via arithmetic progressions. In Proceedings of the nineteenth annual ACM symposium on Theory of computing(STOC ’87). ACM, New York, NY, USA, 1–6.Google ScholarDigital Library
- Pierluigi Crescenzi, Clémence Magnien, and Andrea Marino. 2020. Finding top-k nodes for temporal closeness in large temporal graphs. Algorithms 13, 9 (2020), 211.Google ScholarCross Ref
- Kousik Das, Sovan Samanta, and Madhumangal Pal. 2018. Study on centrality measures in social networks: A survey. Social Network Analysis and Mining 8, 1 (2018), 13.Google ScholarCross Ref
- Linton C. Freeman. 1977. A Set of Measures of Centrality Based on Betweenness. Sociometry 40(1977), 35–41.Google ScholarCross Ref
- Sergio Gómez. 2019. Centrality in networks: finding the most important nodes. In Business and Consumer Analytics: New Ideas. Springer, 401–433.Google Scholar
- Felipe Grando, Diego Noble, and Luis C. Lamb. 2016. An analysis of centrality measures for complex and social networks. In 2016 IEEE Global Communications Conference (GLOBECOM). IEEE, 1–6.Google ScholarDigital Library
- Peter Grindrod, Mark C. Parsons, Desmond J. Higham, and Ernesto Estrada. 2011. Communicability across evolving networks. Physical Review E 83, 4 (2011), 046120.Google ScholarCross Ref
- Shahrzad Haddadan, Cristina Menghini, Matteo Riondato, and Eli Upfal. 2021. RePBubLik: Reducing Polarized Bubble Radius with Link Insertions. In Proceedings of the 14th ACM International Conference on Web Search and Data Mining. 139–147.Google ScholarDigital Library
- Frank Harary and Robert Z. Norman. 1960. Some properties of line digraphs. Rendiconti del Circolo Matematico di Palermo 9, 2 (May 1960), 161–168.Google Scholar
- Tad Hogg and Kristina Lerman. 2012. Social dynamics of digg. EPJ Data Science 1, 1 (2012), 5.Google ScholarCross Ref
- Petter Holme. 2015. Modern temporal network theory: a colloquium. The European Physical Journal B 88, 9 (2015), 234.Google ScholarCross Ref
- Lorenzo Isella, Juliette Stehlé, Alain Barrat, Ciro Cattuto, Jean-François Pinton, and Wouter Van den Broeck. 2011. What’s in a crowd? Analysis of face-to-face behavioral networks. Journal of Theoretical Biology 271, 1 (2011), 166–180.Google ScholarCross Ref
- Leo Katz. 1953. A new status index derived from sociometric analysis. Psychometrika 18, 1 (1953), 39–43.Google ScholarCross Ref
- David Kempe, Jon M. Kleinberg, and Éva Tardos. 2003. Maximizing the spread of influence through a social network. In Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Lise Getoor, Ted E. Senator, Pedro M. Domingos, and Christos Faloutsos (Eds.). ACM, 137–146.Google ScholarDigital Library
- Maurice G. Kendall. 1938. A new measure of rank correlation. Biometrika 30, 1/2 (1938), 81–93.Google ScholarCross Ref
- Gaurav Khanna, Sanjay K. Chaturvedi, and Sieteng Soh. 2020. Two-terminal reliability analysis for time-evolving and predictable delay-tolerant networks. Recent Advances in Electrical & Electronic Engineering (Formerly Recent Patents on Electrical & Electronic Engineering) 13, 2(2020), 236–250.Google ScholarCross Ref
- Hyoungshick Kim and Ross Anderson. 2012. Temporal node centrality in complex networks. Physical Review E 85, 2 (2012), 026107.Google ScholarCross Ref
- Bryan Klimt and Yiming Yang. 2004. The enron corpus: A new dataset for email classification research. In European Conference on Machine Learning. Springer, 217–226.Google ScholarDigital Library
- Andrea Landherr, Bettina Friedl, and Julia Heidemann. 2010. A critical review of centrality measures in social networks. Business & Information Systems Engineering 2, 6 (2010), 371–385.Google ScholarCross Ref
- Matthieu Latapy, Tiphaine Viard, and Clémence Magnien. 2018. Stream graphs and link streams for the modeling of interactions over time. Soc. Netw. Anal. Min. 8, 1 (2018), 61:1–61:29.Google Scholar
- Qingkai Liang and Eytan Modiano. 2016. Survivability in time-varying networks. IEEE Transactions on Mobile Computing 16, 9 (2016), 2668–2681.Google ScholarDigital Library
- Massimo Marchiori and Vito Latora. 2000. Harmony in the small-world. Physica A: Statistical Mechanics and its Applications 285, 3-4(2000), 539–546.Google Scholar
- Rossana Mastrandrea, Julie Fournet, and Alain Barrat. 2015. Contact patterns in a high school: a comparison between data collected using wearable sensors, contact diaries and friendship surveys. PloS one 10, 9 (2015), e0136497.Google ScholarCross Ref
- Alan E. Mislove. 2009. Online social networks: measurement, analysis, and applications to distributed information systems. Ph. D. Dissertation. Rice University.Google Scholar
- Alan E. Mislove, Massimiliano Marcon, P. Krishna Gummadi, Peter Druschel, and Bobby Bhattacharjee. 2007. Measurement and analysis of online social networks. In Proceedings of the 7th ACM SIGCOMM Internet Measurement Conference, IMC. ACM, 29–42.Google ScholarDigital Library
- Petra Mutzel and Lutz Oettershagen. 2019. On the enumeration of bicriteria temporal paths. In International Conference on Theory and Applications of Models of Computation. Springer, 518–535.Google ScholarDigital Library
- Mark E. J. Newman. 2005. A measure of betweenness centrality based on random walks. Soc. Networks 27, 1 (2005), 39–54.Google ScholarCross Ref
- Mark E. J. Newman. 2010. Networks: An Introduction. Oxford University Press.Google ScholarCross Ref
- Giang Hoang Nguyen, John Boaz Lee, Ryan A. Rossi, Nesreen K. Ahmed, Eunyee Koh, and Sungchul Kim. 2018. Continuous-time dynamic network embeddings. In Companion Proceedings of the The Web Conference 2018. 969–976.Google ScholarDigital Library
- Vincenzo Nicosia, John Tang, Cecilia Mascolo, Mirco Musolesi, Giovanni Russo, and Vito Latora. 2013. Graph metrics for temporal networks. In Temporal Networks. Springer, 15–40.Google Scholar
- Lutz Oettershagen, Nils M. Kriege, Christopher Morris, and Petra Mutzel. 2020. Temporal Graph Kernels for Classifying Dissemination Processes. In Proceedings of the 2020 SIAM International Conference on Data Mining. SIAM, 496–504.Google ScholarCross Ref
- Lutz Oettershagen and Petra Mutzel. 2020. Efficient Top-k Temporal Closeness Calculation in Temporal Networks. In 2020 IEEE International Conference on Data Mining (ICDM). IEEE, 402–411.Google Scholar
- Lutz Oettershagen and Petra Mutzel. 2022. Computing top-k temporal closeness in temporal networks. Knowledge and Information Systems(2022), 1–29.Google Scholar
- Tore Opsahl and Pietro Panzarasa. 2009. Clustering in weighted networks. Social networks 31, 2 (2009), 155–163.Google Scholar
- Lawrence Page, Sergey Brin, Rajeev Motwani, and Terry Winograd. 1999. The PageRank Citation Ranking: Bringing Order to the Web.Technical Report 1999-66. Stanford InfoLab. Previous number = SIDL-WP-1999-0120.Google Scholar
- Pietro Panzarasa, Tore Opsahl, and Kathleen M. Carley. 2009. Patterns and dynamics of users’ behavior and interaction: Network analysis of an online community. Journal of the American Society for Information Science and Technology 60, 5 (2009), 911–932.Google ScholarDigital Library
- Ashwin Paranjape, Austin R. Benson, and Jure Leskovec. 2017. Motifs in temporal networks. In Proceedings of the Tenth ACM International Conference on Web Search and Data Mining. 601–610.Google ScholarDigital Library
- Matthew Richardson, Rakesh Agrawal, and Pedro Domingos. 2003. Trust management for the semantic web. In The Semantic Web-ISWC 2003. Springer, 351–368.Google ScholarDigital Library
- Francisco Aparecido Rodrigues. 2019. Network centrality: An introduction. In A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems. Springer, 177–196.Google Scholar
- José Ricardo Furlan Ronqui and Gonzalo Travieso. 2015. Analyzing complex networks through correlations in centrality measurements. Journal of Statistical Mechanics: Theory and Experiment 2015, 5(2015), P05030.Google ScholarCross Ref
- Polina Rozenshtein and Aristides Gionis. 2016. Temporal PageRank. In Machine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2016, Vol. 9852. Springer, 674–689.Google Scholar
- Nicola Santoro, Walter Quattrociocchi, Paola Flocchini, Arnaud Casteigts, and Frederic Amblard. 2011. Time-varying graphs and social network analysis: Temporal indicators and metrics. arXiv preprint arXiv:1102.0629(2011).Google Scholar
- Akrati Saxena and Sudarshan Iyengar. 2020. Centrality Measures in Complex Networks: A Survey. CoRR abs/2011.07190(2020). arxiv:2011.07190https://arxiv.org/abs/2011.07190Google Scholar
- Jun Sun, Jérôme Kunegis, and Steffen Staab. 2016. Predicting User Roles in Social Networks Using Transfer Learning with Feature Transformation. In IEEE International Conference on Data Mining Workshops, ICDM Workshops. IEEE Computer Society, 128–135.Google Scholar
- John Tang, Ilias Leontiadis, Salvatore Scellato, Vincenzo Nicosia, Cecilia Mascolo, Mirco Musolesi, and Vito Latora. 2013. Applications of temporal graph metrics to real-world networks. In Temporal Networks. Springer, 135–159.Google Scholar
- John Tang, Mirco Musolesi, Cecilia Mascolo, Vito Latora, and Vincenzo Nicosia. 2010. Analysing information flows and key mediators through temporal centrality metrics. In Proc. 3rd Workshop on Social Network Systems. 1–6.Google ScholarDigital Library
- Ioanna Tsalouchidou, Ricardo Baeza-Yates, Francesco Bonchi, Kewen Liao, and Timos Sellis. 2019. Temporal betweenness centrality in dynamic graphs. International Journal of Data Science and Analytics (2019), 1–16.Google Scholar
- Philippe Vanhems, Alain Barrat, Ciro Cattuto, Jean-François Pinton, Nagham Khanafer, Corinne Régis, Byeul-a Kim, Brigitte Comte, and Nicolas Voirin. 2013. Estimating potential infection transmission routes in hospital wards using wearable proximity sensors. PloS one 8, 9 (2013), e73970.Google ScholarCross Ref
- Bimal Viswanath, Alan Mislove, Meeyoung Cha, and Krishna P. Gummadi. 2009. On the evolution of user interaction in facebook. In Proceedings of the 2nd ACM workshop on Online social networks. 37–42.Google ScholarDigital Library
- Robert Wetzker, Carsten Zimmermann, and Christian Bauckhage. 2008. Analyzing social bookmarking systems: A del. icio. us cookbook. In Proceedings of the ECAI 2008 Mining Social Data Workshop. 26–30.Google Scholar
- Scott White and Padhraic Smyth. 2003. Algorithms for estimating relative importance in networks. In Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining. 266–275.Google ScholarDigital Library
- Huanhuan Wu, James Cheng, Silu Huang, Yiping Ke, Yi Lu, and Yanyan Xu. 2014. Path problems in temporal graphs. Proc. VLDB Endowment 7, 9 (2014), 721–732.Google ScholarDigital Library
- Xudong Wu, Luoyi Fu, Zixin Zhang, Huan Long, Jingfan Meng, Xinbing Wang, and Guihai Chen. 2020. Evolving Influence Maximization in Evolving Networks. ACM Trans. Internet Technol. 20, 4, Article 40 (Oct. 2020).Google ScholarDigital Library
Index Terms
- Temporal Walk Centrality: Ranking Nodes in Evolving Networks
Index terms have been assigned to the content through auto-classification.
Recommendations
ONBRA: Rigorous Estimation of the Temporal Betweenness Centrality in Temporal Networks
WWW '22: Proceedings of the ACM Web Conference 2022In network analysis, the betweenness centrality of a node informally captures the fraction of shortest paths visiting that node. The computation of the betweenness centrality measure is a fundamental task in the analysis of modern networks, enabling the ...
Ranking Nodes in Temporal Networks: Eigen Value and Node Degree Growth based
IPMV '20: Proceedings of the 2020 2nd International Conference on Image Processing and Machine VisionCompared with the traditional static network, the temporal networks can describe the events in the network in more detail and comprehensively. The static network only considers the connection between nodes and ignores the process of network development, ...
A Higher-Order Temporal H-Index for Evolving Networks
KDD '23: Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data MiningThe H-index of a node in a static network is the maximum value h such that at least h of its neighbors have a degree of at least h. Recently, a generalized version, the n-th order H-index, was introduced, allowing to relate degree centrality, H-index, ...
Comments