# 7.3. 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.

Next Section - 7.4. An Adjacency Matrix