We analyze three hyper-operations derived from directed graphs, demonstrate the influence of the underlying graph structure on these hyper-operations and study the algebraic properties of the related classes of graphs. The paper also illustrates the relationship between directed graphs and hyper-structures using graph hyper-operations. In addition, we investigate the property of commutativity for an appropriate type of hyper-groupoids and its relationship to properties of directed graphs. Therefore, the paper consists of three sections, section one introduces and investigates three distinct hyper-groupoids derived from hyper-operations on directed graphs, section two discusses the fundamental ideas of directed graphs, and section three elaborates on path, simple path, and ancestry hyper-operations.