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Return connected subgraphs with exactly k vertices #35864

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merged 3 commits into from
Jul 20, 2023
Merged

Return connected subgraphs with exactly k vertices #35864

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ed93eda
Return subgraphs with exactly k vertices
deinst Jun 30, 2023
0dcd557
Fix formatting in documentation of connected_subgraph_iterator
deinst Jun 30, 2023
bbcfe17
Merge branch 'develop' into sized_subgraphs
deinst Jul 8, 2023
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99 changes: 54 additions & 45 deletions src/sage/graphs/base/static_dense_graph.pyx
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Original file line number Diff line number Diff line change
Expand Up @@ -745,7 +745,8 @@ def connected_full_subgraphs(G, edges_only=False, labels=False,


def connected_subgraph_iterator(G, k=None, bint vertices_only=False,
edges_only=False, labels=False, induced=True):
edges_only=False, labels=False, induced=True,
exactly_k=False):
r"""
Return an terator over the induced connected subgraphs of order at most `k`.

Expand Down Expand Up @@ -783,6 +784,10 @@ def connected_subgraph_iterator(G, k=None, bint vertices_only=False,
connected sub(di)graph only or also non-induced sub(di)graphs.
This parameter can be set to ``False`` for simple (di)graphs only.

- ``exactly_k`` -- boolean (default: ``False``); ``True`` if we only
return graphs of order `k`, ``False`` if we return graphs of order
at most `k`.

EXAMPLES::

sage: G = DiGraph([(1, 2), (2, 3), (3, 4), (4, 2)])
Expand Down Expand Up @@ -811,6 +816,8 @@ def connected_subgraph_iterator(G, k=None, bint vertices_only=False,
Subgraph of (): Digraph on 1 vertex,
Subgraph of (): Digraph on 2 vertices,
Subgraph of (): Digraph on 1 vertex]
sage: list(G.connected_subgraph_iterator(k=3, vertices_only=True, exactly_k=True))
[[1, 2, 3], [1, 2, 4], [2, 3, 4]]
sage: list(G.connected_subgraph_iterator(k=2, vertices_only=True))
[[1], [1, 2], [2], [2, 3], [2, 4], [3], [3, 4], [4]]

Expand Down Expand Up @@ -921,14 +928,15 @@ def connected_subgraph_iterator(G, k=None, bint vertices_only=False,
sig_check()

vertices = [int_to_vertex[u]]
if vertices_only:
yield vertices
else:
H = G.subgraph(vertices)
if edges_only:
yield H.edges(sort=False, labels=labels)
if not exactly_k or mk == 1:
if vertices_only:
yield vertices
else:
yield H
H = G.subgraph(vertices)
if edges_only:
yield H.edges(sort=False, labels=labels)
else:
yield H

# We initialize the loop with vertices u in current, {u+1, ..., n-1}
# in left, and N(u) in boundary
Expand Down Expand Up @@ -970,45 +978,46 @@ def connected_subgraph_iterator(G, k=None, bint vertices_only=False,
# We yield that new subset
vertices = [int_to_vertex[a] for a in range(u, n)
if bitset_in(stack.rows[level], a)]
if vertices_only:
yield vertices
else:
H = G.subgraph(vertices)
if induced:
if edges_only:
yield H.edges(sort=False, labels=labels)
else:
yield H
if not exactly_k or bitset_len(current) == mk - 1:
if vertices_only:
yield vertices
else:
# We use a decomposition into biconnected components to
# work on smaller graphs.
if H.is_directed():
blocks = H.to_undirected().blocks_and_cut_vertices()[0]
else:
blocks = H.blocks_and_cut_vertices()[0]
if len(blocks) == 1:
# H is strongly connected or biconnected
yield from connected_full_subgraphs(H, edges_only=edges_only,
labels=labels)
H = G.subgraph(vertices)
if induced:
if edges_only:
yield H.edges(sort=False, labels=labels)
else:
yield H
else:
L = []
for bloc in blocks:
if len(bloc) == 2:
bb = [[e] for e in H.edge_boundary(bloc, bloc, labels=labels)]
if len(bb) == 2:
# H is directed with edges (u, v) and (v, u)
bb.append(H.edge_boundary(bloc, bloc, labels=labels))
L.append(bb)
else:
L.append(connected_full_subgraphs(H.subgraph(vertices=bloc),
edges_only=True, labels=labels))

for edges in product(*L):
good_edges = flatten(edges, ltypes=list)
if edges_only:
yield list(good_edges)
else:
yield H.subgraph(vertices=H, edges=good_edges)
# We use a decomposition into biconnected components to
# work on smaller graphs.
if H.is_directed():
blocks = H.to_undirected().blocks_and_cut_vertices()[0]
else:
blocks = H.blocks_and_cut_vertices()[0]
if len(blocks) == 1:
# H is strongly connected or biconnected
yield from connected_full_subgraphs(H, edges_only=edges_only,
labels=labels)
else:
L = []
for bloc in blocks:
if len(bloc) == 2:
bb = [[e] for e in H.edge_boundary(bloc, bloc, labels=labels)]
if len(bb) == 2:
# H is directed with edges (u, v) and (v, u)
bb.append(H.edge_boundary(bloc, bloc, labels=labels))
L.append(bb)
else:
L.append(connected_full_subgraphs(H.subgraph(vertices=bloc),
edges_only=True, labels=labels))

for edges in product(*L):
good_edges = flatten(edges, ltypes=list)
if edges_only:
yield list(good_edges)
else:
yield H.subgraph(vertices=H, edges=good_edges)

else:
# We cannot extend the current subset, either due to a lack of
Expand Down