about summary refs log tree commit diff
path: root/.venv/lib/python3.12/site-packages/networkx/algorithms/bipartite/covering.py
diff options
context:
space:
mode:
authorS. Solomon Darnell2025-03-28 21:52:21 -0500
committerS. Solomon Darnell2025-03-28 21:52:21 -0500
commit4a52a71956a8d46fcb7294ac71734504bb09bcc2 (patch)
treeee3dc5af3b6313e921cd920906356f5d4febc4ed /.venv/lib/python3.12/site-packages/networkx/algorithms/bipartite/covering.py
parentcc961e04ba734dd72309fb548a2f97d67d578813 (diff)
downloadgn-ai-4a52a71956a8d46fcb7294ac71734504bb09bcc2.tar.gz
two version of R2R are here HEAD master
Diffstat (limited to '.venv/lib/python3.12/site-packages/networkx/algorithms/bipartite/covering.py')
-rw-r--r--.venv/lib/python3.12/site-packages/networkx/algorithms/bipartite/covering.py57
1 files changed, 57 insertions, 0 deletions
diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/bipartite/covering.py b/.venv/lib/python3.12/site-packages/networkx/algorithms/bipartite/covering.py
new file mode 100644
index 00000000..f937903e
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/algorithms/bipartite/covering.py
@@ -0,0 +1,57 @@
+"""Functions related to graph covers."""
+
+import networkx as nx
+from networkx.algorithms.bipartite.matching import hopcroft_karp_matching
+from networkx.algorithms.covering import min_edge_cover as _min_edge_cover
+from networkx.utils import not_implemented_for
+
+__all__ = ["min_edge_cover"]
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatchable(name="bipartite_min_edge_cover")
+def min_edge_cover(G, matching_algorithm=None):
+    """Returns a set of edges which constitutes
+    the minimum edge cover of the graph.
+
+    The smallest edge cover can be found in polynomial time by finding
+    a maximum matching and extending it greedily so that all nodes
+    are covered.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        An undirected bipartite graph.
+
+    matching_algorithm : function
+        A function that returns a maximum cardinality matching in a
+        given bipartite graph. The function must take one input, the
+        graph ``G``, and return a dictionary mapping each node to its
+        mate. If not specified,
+        :func:`~networkx.algorithms.bipartite.matching.hopcroft_karp_matching`
+        will be used. Other possibilities include
+        :func:`~networkx.algorithms.bipartite.matching.eppstein_matching`,
+
+    Returns
+    -------
+    set
+        A set of the edges in a minimum edge cover of the graph, given as
+        pairs of nodes. It contains both the edges `(u, v)` and `(v, u)`
+        for given nodes `u` and `v` among the edges of minimum edge cover.
+
+    Notes
+    -----
+    An edge cover of a graph is a set of edges such that every node of
+    the graph is incident to at least one edge of the set.
+    A minimum edge cover is an edge covering of smallest cardinality.
+
+    Due to its implementation, the worst-case running time of this algorithm
+    is bounded by the worst-case running time of the function
+    ``matching_algorithm``.
+    """
+    if G.order() == 0:  # Special case for the empty graph
+        return set()
+    if matching_algorithm is None:
+        matching_algorithm = hopcroft_karp_matching
+    return _min_edge_cover(G, matching_algorithm=matching_algorithm)