A directed edge is a fundamental concept in graph theory, representing a connection between two vertices (or nodes) where the relationship has a specific direction. In a directed graph, also known as a digraph, each edge is represented by an arrow pointing from one vertex to another, indicating the flow of information or influence. This directionality is crucial in various applications, such as computer networks, social media analysis, and transportation systems. Directed edges can be used to model relationships like friendship on social platforms, where one user may follow another without reciprocation. They also appear in dependency graphs, where one task must be completed before another can begin. Understanding directed edges helps in analyzing complex systems and optimizing processes.