Matrix-Weighted Graphs: Theory and Applications

by Minh Hoang Trinh, Hyo-Sung Ahn

Overview

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.

Product Details

ISBN-13:	9783032030788
Publisher:	Springer Nature Switzerland
Publication date:	12/24/2025
Series:	Lecture Notes in Control and Information Sciences , #498
Pages:	361
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Minh Hoang Trinh received the B.S. degree in electrical engineering (2013) from Hanoi University of Science and Technology (HUST), Hanoi, Vietnam, the M.S. degree in mechatronics (2015), and the Ph.D. degree in mechanical engineering (2018) both from Gwangju Institute of Science and Technology (GIST), Gwangju, South Korea. In 2016, he was a visiting research student at Technion - Israel Institute of Technology, Haifa, Israel. From 2018 to 2019, he was as a postdoc researcher at GIST. Dr. Trinh worked as a lecturer at Hanoi University of Science and Technology, Hanoi (2019-2023), and a lecturer/researcher at the FPT University, Binh Dinh, Vietnam (2023-2024). His research interests include distributed control of multi-agent systems, graph rigidity theory, and matrix-weighted graphs.

Hyo-Sung Ahn is a professor at the Department of Mechanical and Robotics Engineering, Gwangju Institute of Science and Technology (GIST), Gwangju, Korea. He received the B.S degree in astronomy & atmospheric science from Yonsei University, Seoul, Korea, in 1998, and the Ph.D. degree in electrical engineering from Utah State University, Logan, in 2006. Since July 2007, he has been with the School of Mechatronics and School of Mechanical Engineering, GIST. Before joining GIST, he was a senior researcher with the Electronics and Telecommunications Research Institute, Daejeon, Korea. His research interests include formation control, distributed control, aerospace navigation and control, network localization, and learning control.

Table of Contents

Part I: Graphs and Networks with Matrix-Weights.- Matrix-Weighted Graphs.- Matrix-Weighted Laplacian.- Physical Interpretation and Motivational Examples.- Part II: Algorithms.- Connectivity.- Spanning Trees.- Quantitative Measures.- Part III: Control.- Matrix-Weighted Consensus.- Discrete-Time and Randomized Algorithms.- Accelerated Algorithms.- Robustness .- Tracking.- Time-Delays.- Part IV: Applications.- Synchronization.- Scaling Matrices.- Networked Input–Output Analysis.- Bearing-Only Formation Control.