class GraphEdgeSet:
    """
    Assume: All vertices have __hash__ implemented
    and __eq__ implemented
    
    Let |V| be the number of vertices
    and |E| be the number of edges
    
    """
    def __init__(self):
        self.V = set([])
        self.E = set([])
    
    def add_vertex(self, v):
        self.V.add(v)
    
    def add_edge(self, u, v):
        self.E.add((u, v))
        # NOTE: If (u, v) is in edges, we assume
        # that (v, u) is also in edges
    
    def get_neighbors(self, v):
        ## Loop through every edge and see if 
        ## v is in that edge
        ## O(|E|)
        neighbs = set([])
        for (a, b) in self.E:
            if a == v:
                neighbs.add(b)
            elif b == v:
                neighbs.add(a)
        return neighbs
                
    
graph = GraphEdgeSet()
for v in range(5):
    graph.add_vertex(v)
graph.add_edge(0, 1)
graph.add_edge(1, 2)
graph.add_edge(1, 4)
graph.add_edge(4, 3)
graph.add_edge(1, 3)
for v in range(5):
    print(v, graph.get_neighbors(v))

0 {1}
1 {0, 2, 3, 4}
2 {1}
3 {1, 4}
4 {1, 3}