8.1: Directed Graphs

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800px-Directed.svg.png — Figure \(\PageIndex{1}\): A directed graph. (Public Domain; via Wikimedia Commons)

The number of edges with one endpoint on a given vertex is called that vertex's degree. In a directed graph, the number of edges that point to a given vertex is called its in-degree, and the number that point from it is called its out-degree. Often, we may want to be able to distinguish between different nodes and edges. We can associate labels with either. We call such a graph labeled.

Directed Graph Operations

make-graph(): graph

Create a new graph, initially with no nodes or edges.

make-vertex(graph G, element value): vertex

Create a new vertex, with the given value.

make-edge(vertex u, vertex v): edge

Create an edge between u and v. In a directed graph, the edge will flow from u to v.

get-edges(vertex v): edge-set

Returns the set of edges flowing from v

get-neighbors(vertex v): vertex-set

Returns the set of vertices connected to v