I am currently taking a graduate logic course on Modal Logic and I can't help notice that there are a certain class of graphs characterized by the modal axioms such as (4) $\Box p \rightarrow \Box \Box p$, (5) $\Diamond p \rightarrow \Box \Diamond p$, or (B) $p \rightarrow \Box \Diamond p$ which can characterize frames as being transitive, Euclidean, and symmetric, respectively. In general, I notice many similarities between the models used in Modal Logic and the graphs in Graph Theory and I'm wondering if anyone knows if there are applications of Modal Logic to Graph Theory, or if one subject might be a special case of the other?

In any case, if anyone has studied this before or knows of any references on the interplay between Modal Logic and Graph Theory I would be very interested to read about it, and if it has not been studied before then I would be interested of any ideas regarding what open research problems could be stated to tackle the correspondence between these two topics. (A category theory perspective on this interplay would also be very interesting)