Picture map of Europe with pins indicating European capital cities

Open Access research with a European policy impact...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by Strathclyde researchers, including by researchers from the European Policies Research Centre (EPRC).

EPRC is a leading institute in Europe for comparative research on public policy, with a particular focus on regional development policies. Spanning 30 European countries, EPRC research programmes have a strong emphasis on applied research and knowledge exchange, including the provision of policy advice to EU institutions and national and sub-national government authorities throughout Europe.

Explore research outputs by the European Policies Research Centre...

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

Full text not available in this repository. Request a copy from the Strathclyde author

Abstract

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.