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International Symposium on Computational Science and Computing

ISCSC 2018 2018: Advances in Computational Science and Computing pp 316–323Cite as

General Quasi-Laplacian Matrix of Weighted Mixed Pseudograph

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 877))

Abstract

Many practical problems can be described as a kind graph model having multiple weighted directed edges, undirected edges and weighted vertices simultaneously however, which are lack of sufficient considerations in previous literatures. We discuss some basic definitions for this more general graph and derive some relevant results for its quasi-Laplacian spectrum. Basic non negative results of its eigenvalues are proposed. Furthermore, we argue some dynamic properties between graph spectral layout and its structural variation. Here two types networks evolutionary manner involving insert of new edge or new vertex are considered. The strictness of related conclusions is guaranteed by theoretical analysis. These initial investigation of weighted mixed pseudograph maybe conduct potential theoretical or applied values for a numerous of practical problems.

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Notes

  1. 1.

    For simplicity of notations, here E includes all edges(unoriented edges) and arcs(oriented edges).

  2. 2.

    Means the weight value of the edge \(\ne 0\).

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant No. 71471084), Open foundation of Wuhan Research Institution of Jianghan University (Grant No. IWHS2016104, and Grant No. jhunwyy 20151204).

Author information

Authors and Affiliations

  1. Jianghan University, Wuhan, 430056, People’s Republic of China

    Xingguang Chen

  2. Nanjing Institute of Technology, Nanjing, 211167, People’s Republic of China

    Zhentao Zhu

Authors
  1. Xingguang Chen
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  2. Zhentao Zhu
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Corresponding author

Correspondence to Xingguang Chen .

Editor information

Editors and Affiliations

  1. Division of Intelligent Future Technologies, Mälardalen University, Västerås, Sweden

    Ning Xiong

  2. School of Information Science and Technology, Hunan University, Changsha, Hunan, China

    Zheng Xiao

  3. School of Computer Science, Hunan Normal University, Changsha, Hunan, China

    Zhao Tong

  4. Hunan University of Chinese Medicine, School of Computer Science, Changsha, Hunan, China

    Jiayi Du

  5. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore

    Lipo Wang

  6. Design and Physical Sciences Brunel, Electronic and Computer Engineering, College of Engineering, Uxbridge, Middlesex, UK

    Maozhen Li

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Chen, X., Zhu, Z. (2019). General Quasi-Laplacian Matrix of Weighted Mixed Pseudograph. In: Xiong, N., Xiao, Z., Tong, Z., Du, J., Wang, L., Li, M. (eds) Advances in Computational Science and Computing. ISCSC 2018 2018. Advances in Intelligent Systems and Computing, vol 877. Springer, Cham. https://doi.org/10.1007/978-3-030-02116-0_37

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