Faster flag complex (#355)

* feat: added complete hypergraph

* tests: added corresponding

* docs: added new function. style: black isort

* review comments

* review comments

* fix docs maths

* perf: faster random_flag_complex by adding only necessary cliques. tests: moved for consistency and added corresponding

* perf: same for flag_complex

* review comments

* style: black

tests/generators/test_nonuniform.py

@@ -67,51 +67,3 @@ def test_random_hypergraph():
     H4 = xgi.random_hypergraph(10, [0.1], order=2, seed=1)
     assert H4.num_nodes == 10
     assert xgi.unique_edge_sizes(H4) == [3]
-
-
-def test_random_simplicial_complex():
-    # seed
-    S1 = xgi.random_simplicial_complex(10, [0.1, 0.001], seed=1)
-    S2 = xgi.random_simplicial_complex(10, [0.1, 0.001], seed=2)
-    S3 = xgi.random_simplicial_complex(10, [0.1, 0.001], seed=2)
-
-    assert S1._edge != S2._edge
-    assert S2._edge == S3._edge
-
-    # wrong input
-    with pytest.raises(ValueError):
-        S1 = xgi.random_simplicial_complex(10, [1, 1.1])
-    with pytest.raises(ValueError):
-        S1 = xgi.random_simplicial_complex(10, [1, -2])
-
-
-def test_random_flag_complex():
-    # seed
-    S1 = xgi.random_flag_complex(10, 0.1, seed=1)
-    S2 = xgi.random_flag_complex(10, 0.1, seed=2)
-    S3 = xgi.random_flag_complex(10, 0.1, seed=2)
-
-    assert S1._edge != S2._edge
-    assert S2._edge == S3._edge
-
-    # wrong input
-    with pytest.raises(ValueError):
-        S1 = xgi.random_flag_complex(10, 1.1)
-    with pytest.raises(ValueError):
-        S1 = xgi.random_flag_complex(10, -2)
-
-
-def test_random_flag_complex_d2():
-    # seed
-    S1 = xgi.random_flag_complex_d2(10, 0.1, seed=1)
-    S2 = xgi.random_flag_complex_d2(10, 0.1, seed=2)
-    S3 = xgi.random_flag_complex_d2(10, 0.1, seed=2)
-
-    assert S1._edge != S2._edge
-    assert S2._edge == S3._edge
-
-    # wrong input
-    with pytest.raises(ValueError):
-        S1 = xgi.random_flag_complex_d2(10, 1.1)
-    with pytest.raises(ValueError):
-        S1 = xgi.random_flag_complex_d2(10, -2)

tests/generators/test_simplicial_complexes.py

@@ -1,4 +1,5 @@
 import networkx as nx
+import pytest
 
 import xgi
 from xgi.exception import XGIError
@@ -21,6 +22,7 @@ def test_flag_complex():
 
     assert S.edges.members() == simplices_3
 
+    # ps
     S1 = xgi.flag_complex(G, ps=[1], seed=42)
     S2 = xgi.flag_complex(G, ps=[0.5], seed=42)
     S3 = xgi.flag_complex(G, ps=[0], seed=42)
@@ -29,6 +31,7 @@ def test_flag_complex():
     assert S2.edges.members() == simplices_2
     assert S3.edges.members() == simplices_2
 
+    # complete graph
     G1 = nx.complete_graph(4)
     S4 = xgi.flag_complex(G1)
     S5 = xgi.flag_complex(G1, ps=[1])
@@ -44,3 +47,116 @@ def test_flag_complex_d2():
     S2 = xgi.flag_complex_d2(G)
 
     assert set(S.edges.members()) == set(S2.edges.members())
+
+
+def test_random_simplicial_complex():
+    # seed
+    S1 = xgi.random_simplicial_complex(10, [0.1, 0.001], seed=1)
+    S2 = xgi.random_simplicial_complex(10, [0.1, 0.001], seed=2)
+    S3 = xgi.random_simplicial_complex(10, [0.1, 0.001], seed=2)
+
+    assert S1._edge != S2._edge
+    assert S2._edge == S3._edge
+
+    # wrong input
+    with pytest.raises(ValueError):
+        S1 = xgi.random_simplicial_complex(10, [1, 1.1])
+    with pytest.raises(ValueError):
+        S1 = xgi.random_simplicial_complex(10, [1, -2])
+
+
+def test_random_flag_complex():
+
+    S = xgi.random_flag_complex(10, 0.4, seed=2)
+    simplices = {
+        frozenset({0, 4}),
+        frozenset({0, 7}),
+        frozenset({1, 8}),
+        frozenset({2, 5}),
+        frozenset({2, 9}),
+        frozenset({3, 5}),
+        frozenset({3, 6}),
+        frozenset({3, 7}),
+        frozenset({3, 8}),
+        frozenset({4, 5}),
+        frozenset({4, 7}),
+        frozenset({4, 8}),
+        frozenset({6, 7}),
+        frozenset({6, 8}),
+        frozenset({7, 8}),
+        frozenset({0, 4, 7}),
+        frozenset({3, 6, 7}),
+        frozenset({3, 6, 8}),
+        frozenset({3, 7, 8}),
+        frozenset({4, 7, 8}),
+        frozenset({6, 7, 8}),
+    }
+
+    assert set(S.edges.members()) == simplices
+
+    # max_order
+    S = xgi.random_flag_complex(10, 0.4, seed=2, max_order=3)
+    assert set(S.edges.members()) == simplices.union({frozenset({3, 6, 7, 8})})
+
+    # seed
+    S1 = xgi.random_flag_complex(10, 0.1, seed=1)
+    S2 = xgi.random_flag_complex(10, 0.1, seed=2)
+    S3 = xgi.random_flag_complex(10, 0.1, seed=2)
+
+    assert S1._edge != S2._edge
+    assert S2._edge == S3._edge
+
+    # wrong input
+    with pytest.raises(ValueError):
+        S1 = xgi.random_flag_complex(10, 1.1)
+    with pytest.raises(ValueError):
+        S1 = xgi.random_flag_complex(10, -2)
+
+
+def test_random_flag_complex_d2():
+
+    S = xgi.random_flag_complex_d2(10, 0.4, seed=2)
+    simplices = {
+        frozenset({0, 4}),
+        frozenset({0, 7}),
+        frozenset({1, 8}),
+        frozenset({2, 5}),
+        frozenset({2, 9}),
+        frozenset({3, 5}),
+        frozenset({3, 6}),
+        frozenset({3, 7}),
+        frozenset({3, 8}),
+        frozenset({4, 5}),
+        frozenset({4, 7}),
+        frozenset({4, 8}),
+        frozenset({6, 7}),
+        frozenset({6, 8}),
+        frozenset({7, 8}),
+        frozenset({0, 4, 7}),
+        frozenset({3, 6, 7}),
+        frozenset({3, 6, 8}),
+        frozenset({3, 7, 8}),
+        frozenset({4, 7, 8}),
+        frozenset({6, 7, 8}),
+    }
+
+    assert set(S.edges.members()) == simplices
+
+    # consistency with other function
+    S = xgi.random_flag_complex(10, 0.4, seed=3, max_order=2)
+    S0 = xgi.random_flag_complex_d2(10, 0.4, seed=3)
+    assert set(S.edges.members()) == set(S0.edges.members())
+
+    # seed
+    S1 = xgi.random_flag_complex_d2(10, 0.1, seed=1)
+    S2 = xgi.random_flag_complex_d2(10, 0.1, seed=2)
+    S3 = xgi.random_flag_complex_d2(10, 0.1, seed=2)
+
+    assert S1._edge != S2._edge
+    assert S2._edge == S3._edge
+
+    # wrong input
+    with pytest.raises(ValueError):
+        S1 = xgi.random_flag_complex_d2(10, 1.1)
+    with pytest.raises(ValueError):
+        S1 = xgi.random_flag_complex_d2(10, -2)

xgi/generators/classic.py

@@ -217,6 +217,7 @@ def complete_hypergraph(N, order=None, max_order=None, include_singletons=False)
     elif max_order is not None:
         start = 1 if include_singletons else 2
         end = max_order + 1
+        assert end >= start  # can be equal because adding +1 to end below
 
         s = list(nodes)
         edges = chain.from_iterable(combinations(s, r) for r in range(start, end + 1))

xgi/generators/simplicial_complexes.py

@@ -130,26 +130,21 @@ def flag_complex(G, max_order=2, ps=None, seed=None):
         random.seed(seed)
 
     nodes = G.nodes()
+    N = len(nodes)
     edges = G.edges()
 
-    # compute all maximal cliques to fill
-    max_cliques = list(nx.find_cliques(G))
+    cliques_to_add = _cliques_to_fill(G, max_order)
 
     S = SimplicialComplex()
     S.add_nodes_from(nodes)
     S.add_simplices_from(edges)
     if not ps:  # promote all cliques
-        S.add_simplices_from(max_cliques, max_order=max_order)
+        S.add_simplices_from(cliques_to_add, max_order=max_order)
         return S
 
-    if max_order:  # compute subfaces of order max_order (allowed max cliques)
-        max_cliques_to_add = subfaces(max_cliques, order=max_order)
-    else:
-        max_cliques_to_add = max_cliques
-
     # store max cliques per order
     cliques_d = defaultdict(list)
-    for x in max_cliques_to_add:
+    for x in cliques_to_add:
         cliques_d[len(x)].append(x)
 
     # promote cliques with a given probability
@@ -277,13 +272,47 @@ def random_flag_complex(N, p, max_order=2, seed=None):
     G = nx.fast_gnp_random_graph(N, p, seed=seed)
 
     nodes = G.nodes()
-    edges = list(G.edges())
 
-    # compute all triangles to fill
-    max_cliques = list(nx.find_cliques(G))
+    cliques = _cliques_to_fill(G, max_order)
 
     S = SimplicialComplex()
     S.add_nodes_from(nodes)
-    S.add_simplices_from(max_cliques, max_order=max_order)
+    S.add_simplices_from(cliques, max_order=max_order)
 
     return S
+
+
+def _cliques_to_fill(G, max_order):
+    """Return cliques to fill for flag complexes,
+    to be passed to `add_simplices_from`.
+
+    This function was written to speedup flag_complex functions
+    by avoiding adding redundant faces.
+
+    Parameters
+    ----------
+    G : networkx Graph
+        Graph to consider
+    max_order: int or None
+        If None, return maximal cliques. If int, return all cliques
+        up to max_order.
+
+    Returns
+    -------
+    cliques : list
+        List of cliques
+
+    """
+    if max_order is None:
+        cliques = list(nx.find_cliques(G))  # max cliques
+    else:  # avoid adding many unnecessary redundant cliques
+        cliques = []
+        for clique in nx.enumerate_all_cliques(G):  # sorted by size
+            if len(clique) == 1:
+                continue  # don't add singletons
+            if len(clique) <= max_order + 1:
+                cliques.append(clique)
+            else:
+                break  # dont go over whole list if not necessary
+
+    return cliques