# M-accretive Laplacian on a non symmetric graph

## TL;DR

This paper investigates a non self-adjoint Laplacian on directed graphs with asymmetric weights, providing criteria for its m-accretiveness and m-sectoriality, and analyzing the associated heat operator.

## Contribution

It introduces new criteria for m-accretiveness and m-sectoriality of non-symmetric Laplacians on directed graphs, extending understanding of their spectral properties.

## Key findings

- Criteria for m-accretiveness of the non-symmetric Laplacian
- Criteria for m-sectoriality of the non-symmetric Laplacian
- Results on the heat operator related to the non-symmetric Laplacian

## Abstract

We consider a non self-adjoint Laplacian on a directed graph with non symmetric weights on edges. We give a criterion for the m-accretiveness and the m-sectoriality of this Laplacian. Our results are based on a comparison of this operator with its symmetric part for which we can apply dierent results concerning essential self-adjointness of a symmetric Laplace operator on an innite graph. This gives results on the heat operator related to our non-symmetric Laplacian.