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<p class="MsoNormal"><span style="font-family: 'Arial',sans-serif;">This book presents and systematizes results in matrix-weighted graphs, a powerful tool for modeling and analysis of multi-dimensional networked systems. The authors select topics addressing fundamental issues, which they arrange in four parts:</span></p><ul><li class="MsoNormal"><span style="font-family: 'Arial',sans-serif;">graphs and networks with matrix weighting, showing how the matrix-weighted Laplacian forms the foundation for further theoretical developments;</span></li><li class="MsoNormal"><span style="font-family: 'Arial',sans-serif;">development of algorithms for various purposes from the determination of connectivity to quantitative measurement as a key pillar in network design and analysis;</span></li><li class="MsoNormal"><span style="font-family: 'Arial',sans-serif;">control-theoretic integration, providing a framework with the matrix-weighted consensus algorithm playing a central role and which coordinates interacting dynamical agents from each vertex in a cooperative and distributed manner; and</span></li><li class="MsoNormal"><span style="font-family: 'Arial',sans-serif;">applications of matrix-weighted graphs in network synchronization, social networks, networked input–output economics, network localization and formation control.</span></li></ul><p class="MsoNormal"><span style="font-family: 'Arial',sans-serif;">The theoretical results provide a firm foundation for researchers wishing to pursue the study of matrix-weighted networks and related topics and are accessible to graduate students with a background in engineering mathematics.</span></p><p class="MsoNormal"><span style="font-family: 'Arial',sans-serif;">Many of the definitions, analyses, and designs in this book are accompanied by figures, examples and numerical simulations. MATLAB® and Simulink® simulations to assist the reader in understanding and further developing such features are available for download.</span></p><p>&#xa0;</p>

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Matrix-Weighted Graphs

  • 书籍

  • 发表日期：

    2026年

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  • Minh Hoang Trinh,
  • Hyo-Sung Ahn

摘要

This book presents and systematizes results in matrix-weighted graphs, a powerful tool for modeling and analysis of multi-dimensional networked systems. The authors select topics addressing fundamental issues, which they arrange in four parts:

  • graphs and networks with matrix weighting, showing how the matrix-weighted Laplacian forms the foundation for further theoretical developments;
  • development of algorithms for various purposes from the determination of connectivity to quantitative measurement as a key pillar in network design and analysis;
  • control-theoretic integration, providing a framework with the matrix-weighted consensus algorithm playing a central role and which coordinates interacting dynamical agents from each vertex in a cooperative and distributed manner; and
  • applications of matrix-weighted graphs in network synchronization, social networks, networked input–output economics, network localization and formation control.

The theoretical results provide a firm foundation for researchers wishing to pursue the study of matrix-weighted networks and related topics and are accessible to graduate students with a background in engineering mathematics.

Many of the definitions, analyses, and designs in this book are accompanied by figures, examples and numerical simulations. MATLAB® and Simulink® simulations to assist the reader in understanding and further developing such features are available for download.