# 7.6. Implementation¶

Using dictionaries, it is easy to implement the adjacency list in Python. In our implementation of the Graph abstract data type we will create two classes (see Listing 1 and Listing 2), Graph, which holds the master list of vertices, and Vertex, which will represent each vertex in the graph.

Each Vertex uses a dictionary to keep track of the vertices to which it is connected, and the weight of each edge. This dictionary is called connectedTo. The listing below shows the code for the Vertex class. The constructor simply initializes the id, which will typically be a string, and the connectedTo dictionary. The addNeighbor method is used add a connection from this vertex to another. The getConnections method returns all of the vertices in the adjacency list, as represented by the connectedTo instance variable. The getWeight method returns the weight of the edge from this vertex to the vertex passed as a parameter.

Listing 1

class Vertex:
def __init__(self,key):
self.id = key
self.connectedTo = {}

self.connectedTo[nbr] = weight

def __str__(self):
return str(self.id) + ' connectedTo: ' + str([x.id for x in self.connectedTo])

def getConnections(self):
return self.connectedTo.keys()

def getId(self):
return self.id

def getWeight(self,nbr):
return self.connectedTo[nbr]


The Graph class, shown in the next listing, contains a dictionary that maps vertex names to vertex objects. In Figure 4 this dictionary object is represented by the shaded gray box. Graph also provides methods for adding vertices to a graph and connecting one vertex to another. The getVertices method returns the names of all of the vertices in the graph. In addition, we have implemented the __iter__ method to make it easy to iterate over all the vertex objects in a particular graph. Together, the two methods allow you to iterate over the vertices in a graph by name, or by the objects themselves.

Listing 2

class Graph:
def __init__(self):
self.vertList = {}
self.numVertices = 0

self.numVertices = self.numVertices + 1
newVertex = Vertex(key)
self.vertList[key] = newVertex
return newVertex

def getVertex(self,n):
if n in self.vertList:
return self.vertList[n]
else:
return None

def __contains__(self,n):
return n in self.vertList

if f not in self.vertList:
if t not in self.vertList:

def getVertices(self):
return self.vertList.keys()

def __iter__(self):
return iter(self.vertList.values())


Using the Graph and Vertex classes just defined, the following Python session creates the graph in Figure 2. First we create six vertices numbered 0 through 5. Then we display the vertex dictionary. Notice that for each key 0 through 5 we have created an instance of a Vertex. Next, we add the edges that connect the vertices together. Finally, a nested loop verifies that each edge in the graph is properly stored. You should check the output of the edge list at the end of this session against Figure 2.

>>> g = Graph()
>>> for i in range(6):
>>> g.vertList
>>> for v in g:
...    for w in v.getConnections():
...        print("( %s , %s )" % (v.getId(), w.getId()))
...
( 0 , 5 )
( 0 , 1 )
( 1 , 2 )
( 2 , 3 )
( 3 , 4 )
( 3 , 5 )
( 4 , 0 )
( 5 , 4 )
( 5 , 2 )

Next Section - 7.7. The Word Ladder Problem