The focus of this paper lies at the intersection of the fields of tropical algebra and graph theory. In particular the interaction between tropical semirings and directed graphs is investigated. Originally studied in [7], the directed graph of a ring is useful in identifying properties within the algebraic structure of a ring. This work builds off the research done by [2, 5, 1] in constructing directed graphs from rings. However, we will investigate the relationship $(x , y ) → ({min}(x , y ), x + y )$ as defined by the operations of tropical algebra and applied to tropical semirings.