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Merged
merged 2 commits into from
May 28, 2023
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Support networkx 3.1 #35584

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0cf50a2
Support networkx 3.1
tornaria Apr 28, 2023
e599562
Improve `cliques_number_of()` and `cliques_containing_vertices()`
tornaria May 5, 2023
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54 changes: 47 additions & 7 deletions src/sage/graphs/graph.py
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Original file line number Diff line number Diff line change
Expand Up @@ -6786,13 +6786,26 @@ def cliques_number_of(self, vertices=None, cliques=None):
{(0, 0): 2, (0, 1): 3, (0, 2): 2, (1, 0): 2, (1, 1): 3, (1, 2): 2}
sage: F.cliques_number_of(vertices=[(0, 1), (1, 2)])
{(0, 1): 3, (1, 2): 2}
sage: F.cliques_number_of(vertices=(0, 1))
3
sage: G = Graph({0:[1,2,3], 1:[2], 3:[0,1]})
sage: G.show(figsize=[2,2])
sage: G.cliques_number_of()
{0: 2, 1: 2, 2: 1, 3: 1}
"""
import networkx
return networkx.number_of_cliques(self.networkx_graph(), vertices, cliques)
if cliques is None:
cliques = self.cliques_maximal()

if vertices in self: # single vertex
return sum(1 for c in cliques if vertices in c)

from collections import Counter
count = Counter()

for c in cliques:
count.update(c)

return {v : count[v] for v in vertices or self}

@doc_index("Clique-related methods")
def cliques_get_max_clique_graph(self):
Expand Down Expand Up @@ -7493,17 +7506,32 @@ def cliques_containing_vertex(self, vertices=None, cliques=None):

sage: C = Graph('DJ{')
sage: C.cliques_containing_vertex()
{0: [[4, 0]], 1: [[4, 1, 2, 3]], 2: [[4, 1, 2, 3]], 3: [[4, 1, 2, 3]], 4: [[4, 0], [4, 1, 2, 3]]}
{0: [[0, 4]],
1: [[1, 2, 3, 4]],
2: [[1, 2, 3, 4]],
3: [[1, 2, 3, 4]],
4: [[0, 4], [1, 2, 3, 4]]}
sage: C.cliques_containing_vertex(4)
[[0, 4], [1, 2, 3, 4]]
sage: C.cliques_containing_vertex([0, 1])
{0: [[0, 4]], 1: [[1, 2, 3, 4]]}
sage: E = C.cliques_maximal()
sage: E
[[0, 4], [1, 2, 3, 4]]
sage: C.cliques_containing_vertex(cliques=E)
{0: [[0, 4]], 1: [[1, 2, 3, 4]], 2: [[1, 2, 3, 4]], 3: [[1, 2, 3, 4]], 4: [[0, 4], [1, 2, 3, 4]]}
{0: [[0, 4]],
1: [[1, 2, 3, 4]],
2: [[1, 2, 3, 4]],
3: [[1, 2, 3, 4]],
4: [[0, 4], [1, 2, 3, 4]]}

sage: G = Graph({0:[1,2,3], 1:[2], 3:[0,1]})
sage: G.show(figsize=[2,2])
sage: G.cliques_containing_vertex()
{0: [[0, 1, 2], [0, 1, 3]], 1: [[0, 1, 2], [0, 1, 3]], 2: [[0, 1, 2]], 3: [[0, 1, 3]]}
{0: [[0, 1, 2], [0, 1, 3]],
1: [[0, 1, 2], [0, 1, 3]],
2: [[0, 1, 2]],
3: [[0, 1, 3]]}

Since each clique of a 2 dimensional grid corresponds to an edge, the
number of cliques in which a vertex is involved equals its degree::
Expand All @@ -7518,8 +7546,20 @@ def cliques_containing_vertex(self, vertices=None, cliques=None):
sage: sorted(sorted(x for x in L) for L in d[(0, 1)])
[[(0, 0), (0, 1)], [(0, 1), (0, 2)], [(0, 1), (1, 1)]]
"""
import networkx
return networkx.cliques_containing_node(self.networkx_graph(), vertices, cliques)
if cliques is None:
cliques = self.cliques_maximal()

if vertices in self: # single vertex
return [c for c in cliques if vertices in c]

from collections import defaultdict
d = defaultdict(list)

for c in cliques:
for v in c:
d[v].append(c)

return {v : d[v] for v in vertices or self}

@doc_index("Clique-related methods")
def clique_complex(self):
Expand Down