Kruskal's algorithm: test if new edge creates a circle

Question

I'm trying to implement kruskal's algorithm in Python 3.7.

So I wrote a programm "bfs" to do breadth first search which I want to use to check that the edges that are added to the minimum spanning tree in kruskal's algorithm don't create a circle.

from collections import deque #we import a queue structure
def bfs(G, startnode, endnode=None):
 B = {startnode}
 Q = deque([startnode])
 L = []
 while Q:
     v = Q.pop()
     L.append(v)
     #If a final node was specified we will end the search there (including the final node)
     if v == endnode:
         break
     for neighbor in G.neighbors(v):
         if not neighbor in B:
             B.add(neighbor)
             Q.appendleft(neighbor)
 return L  

The code above should be correct and is posted for the sake of completness. Following up we have kruskal's algorithm implementation:

import networkx as nx 
def kruskal_bfs(G):
V =nx.Graph()
edges=sorted(G.edges(data=True), key=lambda t: t[2].get('weight', 1)) #sorts the edges (from stackoverflow)
E_F = set([]) #mimimum spanning tree

for edge in edges:
    E_F.add((edge[0],edge[1])) #add edge to the mimumum spanning tree
    V.add_edges_from(list(E_F)) #combine it with the nodes for bfs
    startnode = edge[0]
    if bfs(V,startnode) == bfs(V, ):
        E_F.remove(edge)
    V.remove_edges_from(list(V.edges())) #reset edges of V
return E_F

The part where I have if bfs(V,startnode) == bfs(V, ): is where I'm kinda stuck, how can I complete this if condition. I tried extending bfs to include some form of "circle detection". That did not work however.

Answer 1

Instead of adding the edge and checking for a circle, compare the trees before you add the edge and add it only if the vertices are not connected. Also, working with UNION-FIND will be more efficient.