Group for Research in Decision Analysis

Path Laplacians in Graphs and Networks. Theory and Applications

Ernesto Estrada University of Strathclyde Glasgow, United Kingdom

I will motivate the introduction of a generalization of the graph Laplacian by using paths on graphs. I will consequently extend the concepts of graph connectivity. Then, I will prove a few results about the path Laplacian matrices for simple graphs. Finally, I will show how this new concept is useful for extending the model of network consensus dynamics and some of the consecuences that this have for the analysis of real-world systems.