How to find all connected subgraph of a graph in networkx?

Question

I'm developing a python application, and i want to list all possible connected subgraph of any size and starting from every node using NetworkX.

I just tried using combinations() from itertools library to find all possible combination of nodes but it is very too slow because it searchs also for not connected nodes:

for r in range(0,NumberOfNodes)
for SG in (G.subgraph(s) for s in combinations(G,r):
    if (nx.is_connected(SG)):
        nx.draw(SG,with_labels=True)
        plt.show()

The actual output is correct. But i need another way faster to do this, because all combinations of nodes with a graph of 50 nodes and 8 as LenghtTupleToFind are up to 1 billion (n! / r! / (n-r)!) but only a minimal part of them are connected subgraph so are what i am interested in. So, it's possible to have a function for do this?

Sorry for my english, thank you in advance

EDIT:

As an example:

so, the results i would like to have:

[0]
[0,1]
[0,2]
[0,3]
[0,1,4]
[0,2,5]
[0,2,5,4]
[0,1,4,5]
[0,1,2,4,5]
[0,1,2,3]
[0,1,2,3,5]
[0,1,2,3,4]
[0,1,2,3,4,5]
[0,3,2]
[0,3,1]
[0,3,2]
[0,1,4,2]

and all combination that generates a connected graph

Answer 1

I had the same requirements and ended up using this code, super close to what you were doing. This code yields exactly the input you asked for.

import networkx as nx
import itertools

G = you_graph
all_connected_subgraphs = []

# here we ask for all connected subgraphs that have at least 2 nodes AND have less nodes than the input graph
for nb_nodes in range(2, G.number_of_nodes()):
    for SG in (G.subgraph(selected_nodes) for selected_nodes in itertools.combinations(G, nb_nodes)):
        if nx.is_connected(SG):
            print(SG.nodes)
            all_connected_subgraphs.append(SG)