You may be interested in "Functorial Approach to Graph and Hypergraph Theory" by M. Schmidt. The paper looks at monoid actions as two object categories and then takes presheaves on these. It contains more than your average paper on categorical constructions on graphs. It is a generalization of the ideas contained in the paper "Categorical Constructions in Graph Theory" by Bumby and Latch.

You may be interested in "Functorial Approach to Graph and Hypergraph Theory" by M. Schmidt. It contains plenty of adjunctions and gives examples of concrete constructions. It contains more than your average paper on categorical constructions on graphs. It is a generalization of the ideas contained in the paper "Categorical Constructions in Graph Theory" by Bumby and Latch. Even if it doesn't have exactly what you are looking for, it is an interesting look.

You may be interested in "Functorial Approach to Graph and Hypergraph Theory" . The paper looks at monoid actions as two object categories and then takes presheaves on these. It contains more than your average paper on categorical constructions on graphs. It is a generalization of the ideas contained in the paper "Categorical Constructions in Graph Theory" by Bumby and Latch.

You may be interested in "Functorial Approach to Graph and Hypergraph Theory" by M. Schmidt. The paper looks at monoid actions as two object categories and then takes presheaves on these. It contains more than your average paper on categorical constructions on graphs. It is a generalization of the ideas contained in the paper "Categorical Constructions in Graph Theory" by Bumby and Latch.