Thanks for the suggestions, everyone, I guess I just needed the right vocabulary! Since under the linked answers, a couple of people asked for code to implement all of this, I thought I’d post an answer for future reference. Apparently, the concept of *strongly* connected components is not defined for non-directed graphs, so the solution is to look for connected components.

For my answer, I adjusted the code found here: https://www.geeksforgeeks.org/connected-components-in-an-undirected-graph/

It just requires reformulating `l`

has integers, rather than strings:

```
class Graph:
# init function to declare class variables
def __init__(self, V):
self.V = V
self.adj = [[] for i in range(V)]
def DFSUtil(self, temp, v, visited):
# Mark the current vertex as visited
visited[v] = True
# Store the vertex to list
temp.append(v)
# Repeat for all vertices adjacent
# to this vertex v
for i in self.adj[v]:
if visited[i] == False:
# Update the list
temp = self.DFSUtil(temp, i, visited)
return temp
# method to add an undirected edge
def addEdge(self, v, w):
self.adj[v].append(w)
self.adj[w].append(v)
# Method to retrieve connected components
# in an undirected graph
def connectedComponents(self):
visited = []
cc = []
for i in range(self.V):
visited.append(False)
for v in range(self.V):
if visited[v] == False:
temp = []
cc.append(self.DFSUtil(temp, v, visited))
return cc
```

Now we can run

```
l = [[0, 1],
[0, 2],
[1, 2],
[2, 3],
[4, 5],
[5, 6],
[7, 8]]
g = Graph(
max([item for sublist in l for item in sublist])+1
)
for sl in l:
g.addEdge(sl[0], sl[1])
cc = g.connectedComponents()
print("Following are connected components")
print(cc)
```

And we get:

```
Following are connected components
[[0, 1, 2, 3], [4, 5, 6], [7, 8]]
```

We can then go back and group the original list:

```
result = []
for sublist in cc:
bucket = [x for x in l if any(y in x for y in sublist)]
result.append(bucket)
```

Output:

```
[[[0, 1], [0, 2], [1, 2], [2, 3]], [[4, 5], [5, 6]], [[7, 8]]]
```

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