research-article

On Scalable Computation of Graph Eccentricities

Authors:

Xuemin LinAuthors Info & Claims

SIGMOD '22: Proceedings of the 2022 International Conference on Management of Data

Pages 904 - 916

https://doi.org/10.1145/3514221.3517874

Published: 11 June 2022 Publication History

Abstract

Given a graph, eccentricity measures the distance from each node to its farthest node. Eccentricity indicates the centrality of each node and collectively encodes fundamental graph properties: the radius and the diameter --- the minimum and maximum eccentricity, respectively, over all the nodes in the graph. Computing the eccentricities for all the graph nodes, however, is challenging in theory: any approach shall either complete in quadratic time or introduce a 1/3 relative error under certain hypotheses. In practice, the state-of-the-art approach PLLECC in computing exact eccentricities relies heavily on a precomputed all-pair-shortest-distance index whose expensive construction refrains PLLECC from scaling up. This paper provides insights to enable scalable exact eccentricity computation that does not rely on any index. The proposed algorithm IFECC handles billion-scale graphs that no existing approach can process and achieves up to two orders of magnitude speedup over PLLECC. As a by-product, IFECC can be terminated at any time during execution to produce approximate eccentricities, which is empirically more stable and reliable than KBFS, the state-of-the-art algorithm for approximately computing eccentricities.

References

[1]

Donald Aingworth, Chandra Chekuri, Piotr Indyk, and Rajeev Motwani. 1999. Fast estimation of diameter and shortest paths (without matrix multiplication). SIAM J. Comput., Vol. 28, 4 (1999), 1167--1181.

Digital Library

[2]

Takuya Akiba, Yoichi Iwata, and Yuki Kawata. 2015. An exact algorithm for diameters of large real directed graphs. In International Symposium on Experimental Algorithms. Springer, 56--67.

Digital Library

[3]

Takuya Akiba, Yoichi Iwata, and Yuichi Yoshida. 2013. Fast exact shortest-path distance queries on large networks by pruned landmark labeling. In Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data. 349--360.

Digital Library

[4]

Réka Albert, Hawoong Jeong, and Albert-László Barabási. 1999. Diameter of the world-wide web. nature, Vol. 401, 6749 (1999), 130--131.

[5]

Syed Shafat Ali, Tarique Anwar, and Syed Afzal Murtaza Rizvi. 2020. A revisit to the infection source identification problem under classical graph centrality measures. Online Social Networks and Media, Vol. 17 (2020), 100061.

[6]

Paulo Sérgio Almeida, Carlos Baquero, and Alcino Cunha. 2012. Fast distributed computation of distances in networks. In 2012 IEEE 51st IEEE Conference on Decision and Control (CDC). IEEE, 5215--5220.

[7]

Paolo Boldi, Marco Rosa, Massimo Santini, and Sebastiano Vigna. 2011. Layered label propagation: A multiresolution coordinate-free ordering for compressing social networks. In Proceedings of the 20th international conference on World wide web. 587--596.

Digital Library

[8]

Paolo Boldi and Sebastiano Vigna. 2004. The webgraph framework I: compression techniques. In Proceedings of the 13th international conference on World Wide Web. 595--602.

Digital Library

[9]

Arthur Brady and Lenore Cowen. 2006. Compact routing on power law graphs with additive stretch. In 2006 Proceedings of the Eighth Workshop on Algorithm Engineering and Experiments (ALENEX). SIAM, 119--128.

[10]

Shiri Chechik, Daniel H Larkin, Liam Roditty, Grant Schoenebeck, Robert E Tarjan, and Virginia Vassilevska Williams. 2014. Better approximation algorithms for the graph diameter. In Proceedings of the twenty-fifth annual ACM-SIAM symposium on Discrete algorithms. SIAM, 1041--1052.

[11]

Ertugrul N Ciftcioglu, Kevin S Chan, Ananthram Swami, Derya H Cansever, and Prithwish Basu. 2015. Topology control for time-varying contested environments. In MILCOM 2015--2015 IEEE Military Communications Conference. IEEE, 1397--1402.

Digital Library

[12]

Keith Henderson. 2011. Opex: Optimized eccentricity computation in graphs. Technical Report. Lawrence Livermore National Lab.(LLNL), Livermore, CA (United States).

[13]

Keita Iwabuchi, Geoffrey Sanders, Keith Henderson, and Roger Pearce. 2018. Computing exact vertex eccentricity on massive-scale distributed graphs. In 2018 IEEE International Conference on Cluster Computing (CLUSTER). IEEE, 257--267.

[14]

U Kang, Charalampos E Tsourakakis, Ana Paula Appel, Christos Faloutsos, and Jure Leskovec. 2011. Hadi: Mining radii of large graphs. ACM Transactions on Knowledge Discovery from Data (TKDD), Vol. 5, 2 (2011), 1--24.

[15]

Matjavz Krnc, Jean-Sébastien Sereni, Riste vS krekovski, and Zelealem B Yilma. 2020. Eccentricity of networks with structural constraints. Discussiones Mathematicae Graph Theory, Vol. 40, 4 (2020), 1141--1162.

[16]

Jérôme Kunegis. 2013. Konect: the koblenz network collection. In Proceedings of the 22nd International Conference on World Wide Web. 1343--1350.

Digital Library

[17]

Jure Leskovec and Andrej Krevl. 2014. SNAP Datasets: Stanford large network dataset collection.

[18]

Jure Leskovec and Rok Sosivc. 2016. Snap: A general-purpose network analysis and graph-mining library. ACM Transactions on Intelligent Systems and Technology (TIST), Vol. 8, 1 (2016), 1--20.

Digital Library

[19]

Wentao Li, Miao Qiao, Lu Qin, Ying Zhang, Lijun Chang, and Xuemin Lin. 2018. Exacting Eccentricity for Small-World Networks. In 2018 IEEE 34th International Conference on Data Engineering (ICDE). IEEE, 785--796.

[20]

Zhaoxing Li, Xianchao Zhang, Hua Shen, Wenxin Liang, and Zengyou He. 2015. A semi-supervised framework for social spammer detection. In Pacific-Asia Conference on Knowledge Discovery and Data Mining. Springer, 177--188.

[21]

YP Liu, B Yan, Jiamou Liu, HY Su, H Zheng, and YJ Cai. 2018. From the Periphery to the Core: Information Brokerage in an Evolving Network. In IJCAI'18 Twenty-Seventh International Joint Conference on Artificial Intelligence. International Joint Conferences on Artificial Intelligence.

[22]

Linyuan Lü, Duanbing Chen, Xiao-Long Ren, Qian-Ming Zhang, Yi-Cheng Zhang, and Tao Zhou. 2016. Vital nodes identification in complex networks. Physics Reports, Vol. 650 (2016), 1--63.

[23]

Damien Magoni and Jean Jacques Pansiot. 2001. Analysis of the autonomous system network topology. ACM SIGCOMM Computer Communication Review, Vol. 31, 3 (2001), 26--37.

Digital Library

[24]

Maher Mneimneh and Karem Sakallah. 2003. Computing vertex eccentricity in exponentially large graphs: QBF formulation and solution. In International Conference on Theory and Applications of Satisfiability Testing. Springer, 411--425.

[25]

Mark EJ Newman. 2005. A measure of betweenness centrality based on random walks. Social networks, Vol. 27, 1 (2005), 39--54.

[26]

Kazuya Okamoto, Wei Chen, and Xiang-Yang Li. 2008. Ranking of closeness centrality for large-scale social networks. In International workshop on frontiers in algorithmics. Springer, 186--195.

Digital Library

[27]

Georgios A Pavlopoulos, Maria Secrier, Charalampos N Moschopoulos, Theodoros G Soldatos, Sophia Kossida, Jan Aerts, Reinhard Schneider, and Pantelis G Bagos. 2011. Using graph theory to analyze biological networks. BioData mining, Vol. 4, 1 (2011), 10.

[28]

Liam Roditty and Virginia Vassilevska Williams. 2013. Fast approximation algorithms for the diameter and radius of sparse graphs. In Proceedings of the forty-fifth annual ACM symposium on Theory of computing. 515--524.

Digital Library

[29]

Puck Rombach, Mason A Porter, James H Fowler, and Peter J Mucha. 2017. Core-periphery structure in networks (revisited). SIAM Rev., Vol. 59, 3 (2017), 619--646.

Digital Library

[30]

Ryan Rossi and Nesreen Ahmed. 2015. The network data repository with interactive graph analytics and visualization. In Twenty-Ninth AAAI Conference on Artificial Intelligence .

Digital Library

[31]

M Saravanan and GS Vijay Raajaa. 2012. A graph-based churn prediction model for mobile telecom networks. In International Conference on Advanced Data Mining and Applications. Springer, 367--382.

[32]

Julian Shun. 2015. An evaluation of parallel eccentricity estimation algorithms on undirected real-world graphs. In Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. 1095--1104.

Digital Library

[33]

Frank W Takes and Walter A Kosters. 2011. Determining the diameter of small world networks. In Proceedings of the 20th ACM international conference on Information and knowledge management. 1191--1196.

Digital Library

[34]

Frank W. Takes and Walter A. Kosters. 2013. Computing the Eccentricity Distribution of Large Graphs. Algorithms, Vol. 6, 1 (2013), 100--118.

[35]

Manuel Then, Moritz Kaufmann, Fernando Chirigati, Tuan-Anh Hoang-Vu, Kien Pham, Alfons Kemper, Thomas Neumann, and Huy T Vo. 2014. The more the merrier: Efficient multi-source graph traversal. Proceedings of the VLDB Endowment, Vol. 8, 4 (2014), 449--460.

Digital Library

[36]

Turki Turki and Jason TL Wang. 2015. A new approach to link prediction in gene regulatory networks. In International Conference on Intelligent Data Engineering and Automated Learning. Springer, 404--415.

[37]

Kexiang Xu. 2017. Some bounds on the eccentricity-based topological indices of graphs. Bounds in Chemical Graph Theory--Mainstreams, Univ. Kragujevac, Kragujevac (2017), 189--205.

[38]

Ke Xiang Xu, Kinkar Ch Das, and Ayse Dilek Maden. 2016. On a novel eccentricity-based invariant of a graph. Acta Mathematica Sinica, English Series, Vol. 32, 12 (2016), 1477--1493.

[39]

Guihai Yu and Lihua Feng. 2013. On connective eccentricity index of graphs. MATCH Commun. Math. Comput. Chem, Vol. 69, 3 (2013), 611--628.

Cited By

Lu ZZhou XZehmakan AZhang Z(2024)Resistance Eccentricity in Graphs: Distribution, Computation and Optimization2024 IEEE 40th International Conference on Data Engineering (ICDE)10.1109/ICDE60146.2024.00315(4113-4126)Online publication date: 13-May-2024
https://doi.org/10.1109/ICDE60146.2024.00315
Feng ZQiao MCheng H(2023)Modularity-based Hypergraph Clustering: Random Hypergraph Model, Hyperedge-cluster Relation, and ComputationProceedings of the ACM on Management of Data10.1145/36173351:3(1-25)Online publication date: 13-Nov-2023
https://dl.acm.org/doi/10.1145/3617335
D’ascenzo AD’emidio M(2023)Top-k Distance Queries on Large Time-Evolving GraphsIEEE Access10.1109/ACCESS.2023.331660211(102228-102242)Online publication date: 2023
https://doi.org/10.1109/ACCESS.2023.3316602

Index Terms

On Scalable Computation of Graph Eccentricities
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms

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cover image ACM Conferences

SIGMOD '22: Proceedings of the 2022 International Conference on Management of Data

June 2022

2597 pages

ISBN:9781450392495

DOI:10.1145/3514221

General Chair:
Zachary Ives
University of Pennsylvania (USA)
,
Program Chairs:
Angela Bonifati
Lyon 1 University (France)
,
Amr El Abbadi
University of California, Santa Barbara (USA)

Copyright © 2022 ACM.

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Published: 11 June 2022

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Australian Research Council
Ministry of Business, Innovation and Employment
Marsden Fund

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SIGMOD/PODS '22

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SIGMOD

SIGMOD/PODS '22: International Conference on Management of Data

June 12 - 17, 2022

PA, Philadelphia, USA

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Cited By

Lu ZZhou XZehmakan AZhang Z(2024)Resistance Eccentricity in Graphs: Distribution, Computation and Optimization2024 IEEE 40th International Conference on Data Engineering (ICDE)10.1109/ICDE60146.2024.00315(4113-4126)Online publication date: 13-May-2024
https://doi.org/10.1109/ICDE60146.2024.00315
Feng ZQiao MCheng H(2023)Modularity-based Hypergraph Clustering: Random Hypergraph Model, Hyperedge-cluster Relation, and ComputationProceedings of the ACM on Management of Data10.1145/36173351:3(1-25)Online publication date: 13-Nov-2023
https://dl.acm.org/doi/10.1145/3617335
D’ascenzo AD’emidio M(2023)Top-k Distance Queries on Large Time-Evolving GraphsIEEE Access10.1109/ACCESS.2023.331660211(102228-102242)Online publication date: 2023
https://doi.org/10.1109/ACCESS.2023.3316602

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