3.1.8. pywhy_graphs.networkx.is_minimal_m_separator#
- pywhy_graphs.networkx.is_minimal_m_separator(G, x, y, z, i=None, r=None, directed_edge_name='directed', bidirected_edge_name='bidirected', undirected_edge_name='undirected')[source]#
Check if a set ‘z’ is a i-minimal m-separator between ‘x’ and ‘y’.
The function will first check if ‘z’ is a m-separator, and then check if it is minimal. An i-minimal m-separating set is a minimal m-separator that contains i.
This implements the algorithm TESTMINSEP presented in [1] for ancestral mixed graphs, but has been tested to work with non-ancestral graphs.
This implementation differs from the specification of TESTMINSEP in [1] in that we replace the check in line 6 with \(z - i \neq R_x\), and similarly in line 8 with \(z - i \neq R_y\). This change was deemed necessary because in line 4 all nodes in
iare removed, so there cannot be paths fromxtoiin the augmented moralized graph, causing the algorithm to return false when a minimal m-separator existed.- Parameters:
G : mixed-edge-graph
Mixed edge causal graph.
x : node
Node in
G.y : node
Node in
G.z : set
Set of nodes in
Grepresenting the candidate minimal m-separator ofxandy.i : set
Set of nodes which are always included in the found separating set, default is None, which is later set to empty set.
r : set
Largest set of nodes which may be included in the found separating set, default is None, which is later set to all vertices in
G.directed_edge_name : str
Name of the directed edge, default is ‘directed’.
bidirected_edge_name : str
Name of the bidirected edge, default is ‘bidirected’.
undirected_edge_name : str
Name of the undirected edge, default is ‘undirected’.
- Returns:
is_minimal_m_sep : bool
If the set
zis a minimal m-separator, returns True, else returns False.
References