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,Graph, which holds the master list of vertices, andVertex, which will represent each vertex in the graph.

EachVertexuses a dictionary to keep track of the vertices to which it is connected, and the weight of each edge. This dictionary is calledconnectedTo. The listing below shows the code for theVertexclass. The constructor simply initializes theid, which will typically be a string, and theconnectedTodictionary. TheaddNeighbormethod is used add a connection from this vertex to another. ThegetConnectionsmethod returns all of the vertices in the adjacency list, as represented by theconnectedToinstance variable. ThegetWeightmethod returns the weight of the edge from this vertex to the vertex passed as a parameter.

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

    def addNeighbor(self,nbr,weight = 0):
        self.connectedTo[nbr] = weight

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

    def getId(self):
        return self.id

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

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

    def addVertex(self,key):
        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

    def addEdge(self,f,t,cost=0):
        if f not in self.vertList:
            nv = self.addVertex(f)
        if t not in self.vertList:
            nv = self.addVertex(t)
        self.vertList[f].addNeighbor(self.vertList[t], cost)

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

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

>>> g = Graph()
>>> for i in range(6):
...    g.addVertex(i)
>>> g.vertList
{0: <adjGraph.Vertex instance at 0x41e18>,
 1: <adjGraph.Vertex instance at 0x7f2b0>,
 2: <adjGraph.Vertex instance at 0x7f288>,
 3: <adjGraph.Vertex instance at 0x7f350>,
 4: <adjGraph.Vertex instance at 0x7f328>,
 5: <adjGraph.Vertex instance at 0x7f300>}
>>> g.addEdge(0,1,5)
>>> g.addEdge(0,5,2)
>>> g.addEdge(1,2,4)
>>> g.addEdge(2,3,9)
>>> g.addEdge(3,4,7)
>>> g.addEdge(3,5,3)
>>> g.addEdge(4,0,1)
>>> g.addEdge(5,4,8)
>>> g.addEdge(5,2,1)
>>> 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 )

Credits: Interactive Python