Consider the (formal) continuous laplacian problem $- \Delta u = f$ on a bounded domain $\Omega$ with condition on the edge $\partial \Omega$.
In graph theory, a similar problem can be consider : $AU=B$ where the matrix $A$ is the laplacian matrix asociated to the graph and the unknown is a vector $U$ of size the number of nodes of the graph.
I found a lot of books and articles on this two problems and that emphasize their link and common traits.
I am looking for similar references, but rather for the graph version of the continuous problem $- \Delta u + \lambda u = f$ on a bounded domain $\Omega$ with condition on the edge $\partial \Omega$.
I guess the associated graph problem would be something like $(A + \lambda I)U=B$.
Do you have ideas of references that would consider these two problems and compare them ? Thanks for your help.