Path Laplacian matrices : introduction and application to the analysis of consensus in networks
Estrada, Ernesto (2012) Path Laplacian matrices : introduction and application to the analysis of consensus in networks. Linear Algebra and its Applications, 436 (9). pp. 3373-3391. ISSN 0024-3795
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The concept of k-pathLaplacian matrix of a graph is motivated and introduced. The pathLaplacian matrices are a natural generalization of the combinatorial Laplacian of a graph. They are defined by using path matrices accounting for the existence of shortest paths of length k between two nodes. This new concept is motivated by the problem of determining whether every node of a graph can be visited by means of a process consisting of hopping from one node to another separated at distance k from it. The problem is solved by using the multiplicity of the trivial eigenvalue of the corresponding k-pathLaplacian matrix. We apply these matrices to the analysis of the consensus among agents in a networked system. We show how the consensus in different types of network topologies is accelerated by considering not only nearest neighbors but also the influence of long-range interacting ones. Further applications of pathLaplacian matrices in a variety of other fields, e.g., synchronization, flocking, Markov chains, etc., will open a new avenue in algebraic graph theory.
Creators(s): |
Estrada, Ernesto ![]() | Item type: | Article |
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ID code: | 40662 |
Keywords: | graph theory, path matrices, laplacian matrix, consensusanalysis, synchronization, Mathematics, Discrete Mathematics and Combinatorics, Algebra and Number Theory, Geometry and Topology, Numerical Analysis |
Subjects: | Science > Mathematics |
Department: | Faculty of Science > Mathematics and Statistics |
Depositing user: | Pure Administrator |
Date deposited: | 02 Aug 2012 10:42 |
Last modified: | 05 Mar 2021 03:56 |
URI: | https://strathprints.strath.ac.uk/id/eprint/40662 |
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