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Return subgraphs with exactly k vertices
In response to issue #35857 modified connected_subgraph_iterator to just return the subgraphs of order k. - Added a parameter 'exactly_k
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‎src/sage/graphs/base/static_dense_graph.pyx

Lines changed: 54 additions & 45 deletions
Original file line numberDiff line numberDiff line change
@@ -745,7 +745,8 @@ def connected_full_subgraphs(G, edges_only=False, labels=False,
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def connected_subgraph_iterator(G, k=None, bint vertices_only=False,
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edges_only=False, labels=False, induced=True):
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edges_only=False, labels=False, induced=True,
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exactly_k=False):
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r"""
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Return an terator over the induced connected subgraphs of order at most `k`.
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@@ -783,6 +784,10 @@ def connected_subgraph_iterator(G, k=None, bint vertices_only=False,
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connected sub(di)graph only or also non-induced sub(di)graphs.
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This parameter can be set to ``False`` for simple (di)graphs only.
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- ``exactly_k`` -- boolean (default: ``False``); ``True`` if we only
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return graphs of order ``k``, ``False`` if we return graphs of order
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at most ``k``.
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EXAMPLES::
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sage: G = DiGraph([(1, 2), (2, 3), (3, 4), (4, 2)])
@@ -811,6 +816,8 @@ def connected_subgraph_iterator(G, k=None, bint vertices_only=False,
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Subgraph of (): Digraph on 1 vertex,
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Subgraph of (): Digraph on 2 vertices,
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Subgraph of (): Digraph on 1 vertex]
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sage: list(G.connected_subgraph_iterator(k=3, vertices_only=True, exactly_k=True))
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[[1, 2, 3], [1, 2, 4], [2, 3, 4]]
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sage: list(G.connected_subgraph_iterator(k=2, vertices_only=True))
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[[1], [1, 2], [2], [2, 3], [2, 4], [3], [3, 4], [4]]
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@@ -921,14 +928,15 @@ def connected_subgraph_iterator(G, k=None, bint vertices_only=False,
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sig_check()
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vertices = [int_to_vertex[u]]
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if vertices_only:
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yield vertices
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else:
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H = G.subgraph(vertices)
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if edges_only:
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yield H.edges(sort=False, labels=labels)
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if not exactly_k or mk == 1:
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if vertices_only:
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yield vertices
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else:
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yield H
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H = G.subgraph(vertices)
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if edges_only:
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yield H.edges(sort=False, labels=labels)
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else:
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yield H
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# We initialize the loop with vertices u in current, {u+1, ..., n-1}
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# in left, and N(u) in boundary
@@ -970,45 +978,46 @@ def connected_subgraph_iterator(G, k=None, bint vertices_only=False,
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# We yield that new subset
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vertices = [int_to_vertex[a] for a in range(u, n)
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if bitset_in(stack.rows[level], a)]
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if vertices_only:
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yield vertices
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else:
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H = G.subgraph(vertices)
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if induced:
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if edges_only:
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yield H.edges(sort=False, labels=labels)
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else:
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yield H
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if not exactly_k or bitset_len(current) == mk - 1:
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if vertices_only:
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yield vertices
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else:
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# We use a decomposition into biconnected components to
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# work on smaller graphs.
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if H.is_directed():
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blocks = H.to_undirected().blocks_and_cut_vertices()[0]
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else:
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blocks = H.blocks_and_cut_vertices()[0]
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if len(blocks) == 1:
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# H is strongly connected or biconnected
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yield from connected_full_subgraphs(H, edges_only=edges_only,
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labels=labels)
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H = G.subgraph(vertices)
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if induced:
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if edges_only:
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yield H.edges(sort=False, labels=labels)
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else:
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yield H
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else:
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L = []
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for bloc in blocks:
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if len(bloc) == 2:
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bb = [[e] for e in H.edge_boundary(bloc, bloc, labels=labels)]
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if len(bb) == 2:
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# H is directed with edges (u, v) and (v, u)
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bb.append(H.edge_boundary(bloc, bloc, labels=labels))
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L.append(bb)
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else:
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L.append(connected_full_subgraphs(H.subgraph(vertices=bloc),
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edges_only=True, labels=labels))
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1006-
for edges in product(*L):
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good_edges = flatten(edges, ltypes=list)
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if edges_only:
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yield list(good_edges)
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else:
1011-
yield H.subgraph(vertices=H, edges=good_edges)
992+
# We use a decomposition into biconnected components to
993+
# work on smaller graphs.
994+
if H.is_directed():
995+
blocks = H.to_undirected().blocks_and_cut_vertices()[0]
996+
else:
997+
blocks = H.blocks_and_cut_vertices()[0]
998+
if len(blocks) == 1:
999+
# H is strongly connected or biconnected
1000+
yield from connected_full_subgraphs(H, edges_only=edges_only,
1001+
labels=labels)
1002+
else:
1003+
L = []
1004+
for bloc in blocks:
1005+
if len(bloc) == 2:
1006+
bb = [[e] for e in H.edge_boundary(bloc, bloc, labels=labels)]
1007+
if len(bb) == 2:
1008+
# H is directed with edges (u, v) and (v, u)
1009+
bb.append(H.edge_boundary(bloc, bloc, labels=labels))
1010+
L.append(bb)
1011+
else:
1012+
L.append(connected_full_subgraphs(H.subgraph(vertices=bloc),
1013+
edges_only=True, labels=labels))
1014+
1015+
for edges in product(*L):
1016+
good_edges = flatten(edges, ltypes=list)
1017+
if edges_only:
1018+
yield list(good_edges)
1019+
else:
1020+
yield H.subgraph(vertices=H, edges=good_edges)
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else:
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# We cannot extend the current subset, either due to a lack of

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