What distinguishes directed graphs from undirected graphs?

Directed graphs are characterized by the presence of edges that have a specific direction, indicating the relationship or flow from one vertex to another. This directionality means that an edge from vertex A to vertex B is not the same as an edge from vertex B to vertex A; the former implies a one-way connection, while the latter would be a separate edge if it exists. This distinction is central to the functionality of directed graphs in representing relationships where direction matters, such as in social networks, web page links, or transportation routes.

The nature of directed graphs allows for more complex structures and relationships compared to undirected graphs, where edges simply connect vertices without any specified direction. In an undirected graph, if there is an edge connecting two vertices, it implies that the relationship is mutual or bidirectional.

Understanding this aspect of directed graphs helps in applying graph algorithms effectively, such as those used in network flow analysis or pathfinding within directed systems. This is why the presence of edges with directionality is the defining feature that sets directed graphs apart from their undirected counterparts.