Possible Applications of Network Dynamics with the Distance Parameters and the Spectral Properties of its Laplacian Matrix

This study considers n-dimensional network topologies of weights described with distance as a parameter, extending our previous work of the variation of the weight properties of network dynamics. Here we utilize the typical complete graph and star topologies and analyze their behavior when the weigh...

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Bibliographic Details
Main Authors: Hoshiyama, Takako, Shimoyama, Hironori
Format: Conference Proceeding
Language:English
Subjects:
Behavioral sciences
Eigenvalues and eigenfunctions
inverse laws
Laplace equations
Laplacian matrices
network dynamics
Network topology
search probabilities
Smart cities
Stars
Topology
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Summary:This study considers n-dimensional network topologies of weights described with distance as a parameter, extending our previous work of the variation of the weight properties of network dynamics. Here we utilize the typical complete graph and star topologies and analyze their behavior when the weights between agents is inversely proportional to the distance between them. We also consider the cases corresponding to the inverse square law of distance, the inverse cubic law, and more. The inversely proportional law is often appeared in energy, luminosity, field, search probability, etc. We construct a Laplacian matrix that takes distances into account; evaluate the eigenvalue distributions; and analyze the eigenvectors for each system. The behaviors for the maximum eigenvalue of the systems vs the number of agents is characterized by the distance to the powers and the topology of the network. Finally, we discuss the possible applications of the model and the method to the other fields of science and engineering.
ISSN:1949-4106
DOI:10.1109/HONET59747.2023.10374915