8.3. The Graph Abstract Data Type¶

The graph abstract data type (ADT) is defined as follows:

Graph() creates a new, empty graph.
addVertex(vert) adds an instance of Vertex to the graph.
addEdge(fromVert, toVert) Adds a new, directed edge to the graph that connects two vertices.
addEdge(fromVert, toVert, weight) Adds a new, weighted, directed edge to the graph that connects two vertices.
getVertex(vertKey) finds the vertex in the graph named vertKey.
getVertices() returns the list of all vertices in the graph.
in returns True for a statement of the form vertex in graph, if the given vertex is in the graph, False otherwise.

Beginning with the formal definition for a graph there are several ways we can implement the graph ADT in Python. We will see that there are trade-offs in using different representations to implement the ADT described above. There are two well-known implementations of a graph, the adjacency matrix and the adjacency list. We will explain both of these options, and then implement one as a Python class.