Added a _proper_pag function

Signed-off-by: Aryan Roy <[email protected]>

pywhy_graphs/algorithms/pag.py

@@ -7,7 +7,7 @@
 import numpy as np
 
 from pywhy_graphs import ADMG, CPDAG, PAG, StationaryTimeSeriesPAG
-from pywhy_graphs.algorithms.generic import single_source_shortest_mixed_path, valid_mag
+from pywhy_graphs.algorithms.generic import single_source_shortest_mixed_path, has_adc, inducing_path
 from pywhy_graphs.typing import Node, TsNode
 
 from dodiscover.constraint.fcialg import FCI
@@ -1180,12 +1180,61 @@ def pag_to_mag(graph):
 
     return mag
 
-def _proper_pag(G: PAG):
-
-    #check for acyclicity
-    #check for ancestrality
-    #check for maximality
-
+def _proper_pag(G: PAG, L: Optional[set] = None, S: Optional[set] = None):
+    """Checks if the provided graph is a valid Partial ancestral graph (MAG).
+
+    Parameters
+    ----------
+    G : Graph
+        The graph.
+
+    Returns
+    -------
+    is_valid : bool
+        A boolean indicating whether the provided graph is a valid PAG or not.
+
+    """
+
+    if L is None:
+        L = set()
+
+    if S is None:
+        S = set()
+
+    directed_sub_graph = G.sub_directed_graph()
+
+    all_nodes = set(G.nodes)
+
+    # check if there are any undirected edges or more than one edges b/w two nodes
+    for node in all_nodes:
+        nb = set(G.neighbors(node))
+        for elem in nb:
+            edge_data = G.get_edge_data(node, elem)
+            if (edge_data["bidirected"] is not None) and (edge_data["directed"] is not None):
+                return False
+
+    # check if there are any directed cyclces
+    try:
+        nx.find_cycle(directed_sub_graph)  # raises a NetworkXNoCycle error
+        return False
+    except nx.NetworkXNoCycle:
+        pass
+
+    # check if there are any almost directed cycles
+    if has_adc(G):  # if there is an ADC, it's not a valid MAG
+        return False
+
+    # check if there are any inducing paths between non-adjacent nodes
+
+    for source in all_nodes:
+        nb = set(G.neighbors(source))
+        cur_set = all_nodes - nb
+        cur_set.remove(source)
+        for dest in cur_set:
+            out = inducing_path(G, source, dest, L, S)
+            if out[0] is True:
+                return False
+
     return True