Detect cycle in undirected graph

"""
Intuition:

We are exploring an undirected graph using DFS to check if a cycle exists. Because the graph is undirected, every edge works in both directions so while pushing edge(a,b) in the adjacent direction , push a->b and b->a both.
for eg we have only edge ie (0,1) so adjacency matrix would be {0->1, 1->0}.

we will go dfs and the moment we will see any neighbor is having already visited, we will just return the false but there is a problem and the problem when you will go from 0 to 1 then the neighbor of 1 would 0 too which is already visited, so you can't return the False there, so just keep track of the parent and return Cycle only if the neighbor is True and not parent.
"""


from collections import defaultdict
def fun(i,parent,graph,visited):
    visited[i]=True
    for k in graph[i]:
        if visited[k]==True and k!=parent:
            return True
        elif visited[k]==False and fun(k,i,graph,visited):
            return True
    return False

class Solution:
    def isCycle(self, v, edges):
        visited=[False]*v
        graph=defaultdict(list)
        for a,b in edges:
            graph[a].append(b)
            graph[b].append(a)
        for i in range(v):
            if visited[i]==False:
                if fun(i,-1,graph,visited):
                    return True
        return False