Matrix-Weighted Graphs
Theory and Applications
Series: Lecture Notes in Control and Information Sciences;
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Product details:
- Publisher Springer Nature Switzerland
- Date of Publication 22 February 2026
- ISBN 9783032030788
- Binding Hardback
- No. of pages361 pages
- Size 235x155 mm
- Language English
- Illustrations XXIV, 361 p. 84 illus., 68 illus. in color. With online files/update. 698
Categories
Long description:
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.
MoreTable 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.
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