Directed Graph

A directed graph, also known as a digraph, is a complex arrangement made up of points, referred to as "nodes" or "vertices," interconnected by arrows, known as "edges." These arrows denote the direction of connection between nodes.

While a digraph may bear resemblance to a standard graph, the crucial difference lies in the directed nature of its connections. The term "digraph" itself is a shorthand for "directed graph."

In essence, each arrow in a digraph sets forth a one-way relationship from its origin to its destination node, illustrating a directional flow.

Take, for example, an arrow from point A to point C; this signifies a direct path from A to C, without implying a reciprocal route.

In the case of a mixed graph, both nondirectional lines and directed arrows coexist, revealing some relationships as bidirectional, reminiscent of standard graphs, while others maintain a unidirectional nature.

Transforming a digraph by converting all arrows into lines gives rise to an underlying graph. This adjustment morphs all singular directional relationships into bidirectional ones, effectively removing the element of directionality from these connections.

Conversely, initiating with a simple graph and substituting all its lines with arrows results in the creation of a new digraph. This newly formed digraph is termed an orientation of the simple graph, as it assigns a specific direction to each connection.