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Core decomposition and maintenance in weighted graph

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Abstract

Coreness is an important index to reflect the cohesiveness of a graph. The problems of core computation in static graphs and core update in dynamic graphs, known as the core decomposition and core maintenance problems respectively, have been extensively studied in previous work. However, most of these work focus on unweighted graphs. Considering that graphs are weighted in a lot of realistic applications, it is indispensable to extend the coreness to weighted graphs and devise efficient algorithms for weighted core decomposition and weighted core maintenance. In this work, we present a new definition of weighted coreness for vertices in a weighted graph, by taking into account the weights of vertices, which makes the coreness in unweighted graph be a special case. We propose efficient algorithms for both weighted core decomposition and weighted core maintenance problems. The coreness of vertices can be computed in linear time by the proposed decomposition algorithm, while the proposed core maintenance algorithm can process multiple-edge insertions/deletions simultaneously, which greatly reduces the core update time. Comprehensive experiments on both realistic networks and temporal graphs exhibit our algorithms are efficient and scalable.

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Acknowledgements

The work is supported by National Natural Science Foundation of China (No. 61802140, 61972447).

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Authors and Affiliations

  1. Services Computing Technology and System Lab / Big Data Technology and System Lab, Huazhong University of Science and Technology, Wuhan, China

    Wei Zhou, Hong Huang, Qiang-Sheng Hua & Hai Jin

  2. School of Computer Science and Technology, Shandong University, Qingdao, China

    Dongxiao Yu

  3. Institute of Computer Science, University of Goettingen, Goettingen, Germany

    Xiaoming Fu

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  1. Wei Zhou
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  2. Hong Huang
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  3. Qiang-Sheng Hua
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  4. Dongxiao Yu
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Correspondence to Hong Huang.

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Zhou, W., Huang, H., Hua, QS. et al. Core decomposition and maintenance in weighted graph. World Wide Web 24, 541–561 (2021). https://doi.org/10.1007/s11280-020-00857-0

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