How to obtain all the subgraphs from a graph?

Question

How to obtain all the subgraphs of a fixed size from a graph, in pseudocode? (brute force)

Without external libraries if possible. Thanks!

Answer 1

Since a graph is only edges and vertices, find all possible subsets of the vertices and construct all possible subsets of the edges on them.

Answer 2

More or less that would be something along these lines:

GenerateSubgraphs(Graph G):
    powerV = powerset(G.V)
    powerE = powerset(G.E)
    subgraphs = {}
    foreach V in powerV:
        foreach E in powerE:
            accept = true
            foreach edge in E:
                if edge.u not in V or edge.v not in V:
                    accept = false
            if accept:
                subgraphs.insert((V, E))
    return subgraphs

EDIT: Fixed indentation of 'edges.insert' line

EDIT: Removed duplicated graphs