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VEK: a vertex-oriented approach for edge k-core problem

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Abstract

The stability of a network has been widely studied as an important indicator of network status, e.g., reliability and activity. A popular model for measuring the (structural) stability of a network is k-core , the maximal induced subgraph in which every vertex has at least k neighbors in the subgraph. As the size of k-core well estimates the stability of a network, the edge k-core problem is studied to enhance network stability: given a graph G, an integer k and a budget b, add b edges to non-adjacent vertex pairs in G such that the number of vertices in the k-core is maximized. The state-of-the-art solution is a greedy algorithm (named EKC) by finding a promising vertex pair at each iteration, while the algorithm is still not efficient enough on large graphs. In this paper, we propose a novel vertex-oriented heuristic algorithm (named VEK), with a well-designed scoring function to guide the search order. Effective optimization techniques are proposed to prune unpromising candidates and reuse the intermediate results. The experiments on 9 real-life datasets demonstrate the runtime of our proposed VEK is faster than the state-of-the-art algorithm EKC by 1-3 orders of magnitude.

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Availability of data and material

All the datasets used in this paper is public and every one can access to it.

Code Availability

All the source codes will be shared online after the manuscript is accepted.

Notes

  1. http://networkrepository.com/

  2. https://snap.stanford.edu/data/

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Acknowledgments

Fan Zhang is supported by National Natural Science Foundation of China under Grant 62002073, and Guangzhou Basic and Applied Basic Research Foundation under Grant 202102020675.

Funding

The grants declared in Acknowledgements were received to assist with the preparation of this manuscript.

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Authors and Affiliations

  1. East China Normal University, Shanghai, China

    Zhongxin Zhou

  2. Construction Bank of China Qiqihar Branch, Qiqihar, China

    Wenchao Zhang

  3. Guangzhou University, Guangzhou, China

    Fan Zhang

  4. School of Computer Science and Engineering, University of New South Wales, Sydney, Australia

    Deming Chu

  5. School of Minerals and Energy Resources Engineering, University of New South Wales, Sydney, Australia

    Binghao Li

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  1. Zhongxin Zhou
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Correspondence to Fan Zhang.

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This article belongs to the Topical Collection: Special Issue on Large Scale Graph Data Analytics

Guest Editors: Xuemin Lin, Lu Qin, Wenjie Zhang, and Ying Zhang

Zhongxin Zhou and Wenchao Zhang are the joint first authors.

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Zhou, Z., Zhang, W., Zhang, F. et al. VEK: a vertex-oriented approach for edge k-core problem. World Wide Web 25, 723–740 (2022). https://doi.org/10.1007/s11280-021-00907-1

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