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.
Groupe d’études et de recherche en analyse des décisions