Find Subgraphs inside a Connected Component from a NetworkX Graph

Question

I have built a NetworkX Graph containing 50000 Nodes and about 100 Million edges. I have a list of all connected components of this group using nx.connected_components(G) method. This method results in me having clusters of nodes such that each node has a path to reach every other node in that cluster. Now what I want is, in each of these connected components, I want to find subgraphs/sub-clusters such that each of these subgraphs are connected to each other by exactly one edge. Is there a method in NetworkX that I can use directly or any other way in which I can get this done? Sorry I am very new to graph theory so need a little direction.

Answer 1

What you want is called minimum spanning three . Using networkx you can do it like this:

import networkx as nx
import matplotlib.pyplot as plt
G = nx.Graph()
G.add_edges_from([(1,2), (1,3), (2,3), (4,5), (4,6), (5,6)])
nx.draw(nx.minimum_spanning_tree(G), with_labels=True)
plt.show()

However, I'm a little bit in doubt if networkx is able to perform on so many edges according to this benchmark . I have tested connected components algorithm on igraph , it worked for me as well (and, of course, much faster), so you might also like to look for igraph based solutions.

Result

Answer 2

If I understand you correctly, then for each subgraph, you want to find all graph cuts of size 1, ie you want to find all edges, that if taken away partition the graph into two subgraphs. These edges are called bridges and there are efficient algorithms to find them. The implementation in networkx is accessible via networkx.algorithms.bridges.bridges .