Finding Dense and Persistently Expansive Subgraphs
Pages 553 - 556
Abstract
How can we detect a group of individuals whose connectivity persists and even strengthens over time? Despite extensive research on temporal networks, this practically pertinent question has been scantily investigated. In this paper, we formulate the problem of selecting a subset of nodes whose induced subgraph maximizes the overall edge count while abiding by time-aware spectral connectivity constraints. We solve the problem via a semidefinite programming (SDP) relaxation. Our experiments on a broad array of synthetic and real-world data establish the effectiveness of our method and deliver key insights on real-world temporal graphs.
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References
[1]
Alberto Aleta and Yamir Moreno. Multilayer networks in a nutshell. Annual Review of Condensed Matter Physics, 10:45--62, 2019.
[2]
Noga Alon and Vitali D Milman. ??1, isoperimetric inequalities for graphs, and superconcentrators. Journal of Combinatorial Theory, Series B, 38(1):73--88, 1985.
[3]
Sayan Bhattacharya, Monika Henzinger, Danupon Nanongkai, and Charalampos E. Tsourakakis. Space- and time-efficient algorithm for maintaining dense subgraphs on one-pass dynamic streams. In STOC, pages 173--182, 2015.
[4]
Francesco Bonchi, David García-Soriano, Atsushi Miyauchi, and Charalampos E Tsourakakis. Finding densest ??-connected subgraphs. Discrete Applied Mathematics, 305:34--47, 2021.
[5]
Samuel Burer. On the copositive representation of binary and continuous nonconvex quadratic programs. Mathematical Programming, 120(2):479--495, 2009.
[6]
Jeff Cheeger. A lower bound for the smallest eigenvalue of the laplacian. In Problems in analysis, pages 195--200. Princeton University Press, 2015.
[7]
Tianyi Chen, Francesco Bonchi, David García-Soriano, Atsushi Miyauchi, and Charalampos E. Tsourakakis. Dense and well-connected subgraph detection in dual networks. In SIAM Intl Conf. on Data Mining (SDM), pages 361--369, 2022.
[8]
Lizhen Cui, Lingxi Yue, Dong Wen, and Lu Qin. ??-connected cores computation in large dual networks. Data Science and Engineering, 3(4):293--306, 2018.
[9]
Brian C Dean. Shortest paths in fifo time-dependent networks: Theory and algorithms. Rapport technique, Massachusetts Institute of Technology, 13, 2004.
[10]
Steven Diamond and Stephen Boyd. Cvxpy: A python-embedded modeling language for convex optimization. JMLR, 17(1):2909--2913, 2016.
[11]
Arpita Ghosh and Stephen Boyd. Growing well-connected graphs. In 45th IEEE Conference on Decision and Control (DC), pages 6605--6611, 2006.
[12]
Petter Holme and Jari Saramäki. Temporal networks. Physics reports, 519(3):97-- 125, 2012.
[13]
Shlomo Hoory, Nathan Linial, and Avi Wigderson. Expander graphs and their applications. Bulletin of the American Mathematical Society, 43(4):439--561, 2006.
[14]
Richard M Karp. Reducibility among combinatorial problems. In Complexity of computer computations, pages 85--103. Springer, 1972.
[15]
Lauri Kovanen, Márton Karsai, Kimmo Kaski, János Kertész, and Jari Saramäki. Temporal motifs in time-dependent networks. Journal of Statistical Mechanics: Theory and Experiment, 2011(11):P11005, 2011.
[16]
James R. Lee, Shayan Oveis Gharan, and Luca Trevisan. Multiway spectral partitioning and higher-order Cheeger inequalities. J. ACM, 61(6):1--30, 2014.
[17]
Biao Liu, Gao Cong, and Dong Xu. Influence spreading path and its application to the time constrained social influence maximization problem and beyond. IEEE Transactions on Knowledge and Data Engineering (TKDE), 26(8):1904--1917, 2014.
[18]
Naoki Masuda and Petter Holme. Predicting and controlling infectious disease epidemics using temporal networks. F1000prime reports, 5, 2013.
[19]
Raj Kumar Pan and Jari Saramäki. Path lengths, correlations, and centrality in temporal networks. Physical Review E, 84(1):016105, 2011.
[20]
Ashwin Paranjape, Austin R. Benson, and Jure Leskovec. Motifs in temporal networks. In 10th ACM WSDM, pages 601--610, 2017.
[21]
Tiago P. Peixoto. The Netzschleuder network catalogue and repository, 2023.
[22]
Selena Praprotnik and Vladimir Batagelj. Spectral centrality measures in temporal networks. Ars Mathematica Contemporanea, 11(1):11--33, 2015.
[23]
Ryan A. Rossi and Nesreen K. Ahmed. The network data repository with interactive graph analytics and visualization. In AAAI, pages 4292--4293, 2015.
[24]
Konstantinos Semertzidis, Evaggelia Pitoura, Evimaria Terzi, and Panayiotis Tsaparas. Finding lasting dense subgraphs. Data Min. Knowl. Discov., 33(5):1417-- 1445, 2019.
[25]
Daniel A. Spielman. Spectral graph theory and its applications. In IEEE Symposium on Foundations of Computer Science (FOCS), pages 29--38, 2007.
[26]
Daniel A Spielman and Shang-Hua Teng. Spectral sparsification of graphs. SIAM Journal on Computing, 40(4):981--1025, 2011.
[27]
Anton Tsitsulin, Davide Mottin, Panagiotis Karras, Alexander M. Bronstein, and Emmanuel Müller. NetLSD: Hearing the shape of a graph. In 24th ACM SIGKDD Intl Conf. on Knowledge Discovery & Data Mining (KDD), pages 2347--2356, 2018.
[28]
Anton Tsitsulin, Marina Munkhoeva, Davide Mottin, Panagiotis Karras, Ivan V. Oseledets, and Emmanuel Müller. FREDE: Anytime graph embeddings. Proc. VLDB Endow., 14(6):1102--1110, 2021.
[29]
Charalampos E. Tsourakakis, Tianyi Chen, Naonori Kakimura, and Jakub Pachocki. Novel dense subgraph discovery primitives: Risk aversion and exclusion queries. In ECML PKDD, pages 378--394, 2019.
[30]
Eugenio Valdano, Luca Ferreri, Chiara Poletto, and Vittoria Colizza. Analytical computation of the epidemic threshold on temporal networks. Physical Review X, 5(2):021005, 2015.
[31]
Lieven Vandenberghe and Stephen Boyd. Semidefinite programming. SIAM review, 38(1):49--95, 1996.
[32]
Yubao Wu, Ruoming Jin, Xiaofeng Zhu, and Xiang Zhang. Finding dense and connected subgraphs in dual networks. In ICDE, pages 915--926, 2015.
[33]
Fan Zhang, Ying Zhang, Lu Qin, Wenjie Zhang, and Xuemin Lin. When engagement meets similarity: efficient (k, r)-core computation on social networks. arXiv preprint arXiv:1611.03254, 2016.
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- Finding Dense and Persistently Expansive Subgraphs
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Information & Contributors
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Published In
May 2024
1928 pages
ISBN:9798400701726
DOI:10.1145/3589335
- General Chairs:
- Tat-Seng Chua,
- Chong-Wah Ngo,
- Program Chairs:
- Ravi Kumar,
- Hady W. Lauw,
- Roy Ka-Wei Lee
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Published: 13 May 2024
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