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 0024-3795Full text not available in this repository. (Request a copy from the Strathclyde author)
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.
|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:||07 Jan 2017 01:20|