Extracting a single weakly connected component from a network of many weakly connected components?

Question

Hello Mathematica friends!

I've got a network with thousands of edges and vertices, but not all in one connected component. I'm trying to extract specific connected components from the network, and assign them as new variables.

g = Graph[{1 \[UndirectedEdge] 2, 2 \[UndirectedEdge] 3, 1 \[UndirectedEdge] 3, 4 \[UndirectedEdge] 5, 7 \[UndirectedEdge] 6, 8 \[UndirectedEdge] 6, 5 \[UndirectedEdge] 7, 7 \[UndirectedEdge] 8}]

I know it's a disconnected component because of:

WeaklyConnectedGraphQ[g]
False

I know there are two components:

Length[WeaklyConnectedComponents[g]]
2

I know how many vertices are in each component:

Length /@ WeaklyConnectedComponents[g]
{5, 3}

And I know what vertices are in each component:

WeaklyConnectedComponents[g]
{{7, 6, 5, 8, 4}, {3, 2, 1}}

What I don't know is how to a assign on of these components to a new variable to then proceed with analysis on just a single connected component?

Answer 1

I understand that you want the subgraph of g that corresponds to the vertices in one of the w.c.c (say, the first one). How about:

Subgraph[g, First@WeaklyConnectedComponents[g]]

If you want, say, the 13th connected component, just do

Subgraph[g, WeaklyConnectedComponents[g][[13]] ]