Detect Cycle in Undirected Graph using DFS in Python

class Graph:
    def __init__(self):
        # dictionary containing keys that map to the corresponding vertex object
        self.vertices = {}
 
    def add_vertex(self, key):
        """Add a vertex with the given key to the graph."""
        vertex = Vertex(key)
        self.vertices[key] = vertex
 
    def get_vertex(self, key):
        """Return vertex object with the corresponding key."""
        return self.vertices[key]
 
    def __contains__(self, key):
        return key in self.vertices
 
    def add_edge(self, src_key, dest_key, weight=1):
        """Add edge from src_key to dest_key with given weight."""
        self.vertices[src_key].add_neighbour(self.vertices[dest_key], weight)
 
    def add_undirected_edge(self, v1_key, v2_key, weight=1):
        """Add undirected edge (2 directed edges) between v1_key and v2_key with
        given weight."""
        self.add_edge(v1_key, v2_key, weight)
        self.add_edge(v2_key, v1_key, weight)
 
    def does_undirected_edge_exist(self, v1_key, v2_key):
        """Return True if there is an undirected edge between v1_key and v2_key."""
        return (self.does_edge_exist(v1_key, v2_key)
                and self.does_edge_exist(v1_key, v2_key))
 
    def does_edge_exist(self, src_key, dest_key):
        """Return True if there is an edge from src_key to dest_key."""
        return self.vertices[src_key].does_it_point_to(self.vertices[dest_key])
 
    def __iter__(self):
        return iter(self.vertices.values())
 
 
class Vertex:
    def __init__(self, key):
        self.key = key
        self.points_to = {}
 
    def get_key(self):
        """Return key corresponding to this vertex object."""
        return self.key
 
    def add_neighbour(self, dest, weight):
        """Make this vertex point to dest with given edge weight."""
        self.points_to[dest] = weight
 
    def get_neighbours(self):
        """Return all vertices pointed to by this vertex."""
        return self.points_to.keys()
 
    def get_weight(self, dest):
        """Get weight of edge from this vertex to dest."""
        return self.points_to[dest]
 
    def does_it_point_to(self, dest):
        """Return True if this vertex points to dest."""
        return dest in self.points_to
 
 
def is_cycle_present(v, visited):
    """Return True if cycle is present in component containing vertex and put
    all vertices in component in set visited."""
    parent = {v: None}
    return is_cycle_present_helper(v, visited, parent)
 
 
def is_cycle_present_helper(v, visited, parent):
    """Return True if cycle is present in component containing vertex and put
    all vertices in component in set visited. Uses dictionary parent to keep
    track of parents of nodes in the DFS tree."""
    visited.add(v)
    for dest in v.get_neighbours():
        if dest not in visited:
            parent[dest] = v
            if is_cycle_present_helper(dest, visited, parent):
                return True
        else:
            if parent[v] is not dest:
                return True
    return False
 
 
g = Graph()
print('Undirected Graph')
print('Menu')
print('add vertex <key>')
print('add edge <vertex1> <vertex2>')
print('cycle')
print('display')
print('quit')
 
while True:
    do = input('What would you like to do? ').split()
 
    operation = do[0]
    if operation == 'add':
        suboperation = do[1]
        if suboperation == 'vertex':
            key = int(do[2])
            if key not in g:
                g.add_vertex(key)
            else:
                print('Vertex already exists.')
        elif suboperation == 'edge':
            v1 = int(do[2])
            v2 = int(do[3])
            if v1 not in g:
                print('Vertex {} does not exist.'.format(v1))
            elif v2 not in g:
                print('Vertex {} does not exist.'.format(v2))
            else:
                if not g.does_undirected_edge_exist(v1, v2):
                    g.add_undirected_edge(v1, v2)
                else:
                    print('Edge already exists.')
 
    elif operation == 'cycle':
        present = False
        visited = set()
        for v in g:
            if v not in visited:
                if is_cycle_present(v, visited):
                    present = True
                    break
 
        if present:
            print('Cycle present.')
        else:
            print('Cycle not present.')
 
    elif operation == 'display':
        print('Vertices: ', end='')
        for v in g:
            print(v.get_key(), end=' ')
        print()
 
        print('Edges: ')
        for v in g:
            for dest in v.get_neighbours():
                w = v.get_weight(dest)
                print('(src={}, dest={}, weight={}) '.format(v.get_key(),
                                                             dest.get_key(), w))
        print()
 
    elif operation == 'quit':
        break