Connected Vertices in Graph

class Vertex:
    def __init__(self,n):
        self.name=n
        self.neighbours=list()
        
    def addneighbours(self,v):
        if v not in self.neighbours:
            self.neighbours.append(v)
            self.neighbours.sort()
            
class Graph:
    vertices={}
    
    def addvertex(self,vertex):
        if isinstance(vertex, Vertex)and vertex.name not in self.vertices:
            self.vertices[vertex.name]=vertex
            return True
        else:
            return False
    
    def addedge(self,a,b):
        if a in self.vertices and b in self.vertices:
            for key, value in self.vertices.items():
                if key==a:
                    value.addneighbours(b)
                if key==b:
                    value.addneighbours(a)
            return True
        else:
            return False
        
    def printGraph(self):
        for key in sorted(list(self.vertices.keys())):
            print(key+str(self.vertices[key].neighbours))
            
mygraph=Graph()
a= Vertex("A")
mygraph.addvertex(a)
mygraph.addvertex(Vertex('B'))
for i in range(ord('A'),ord('K')):
    mygraph.addvertex(Vertex(chr(i)))
    
edges=['AB','AE','BF','CG','DE','DH','EH','FG','FI','FJ','GJ','HI']
for edge in edges:
    mygraph.addedge(edge[:1],edge[1:])
    
mygraph.printGraph()