import re
from queue import LifoQueue
import networkx as nx
import numpy as np
from networkx.algorithms.dag import is_directed_acyclic_graph
from networkx.algorithms.shortest_paths.generic import shortest_path
from dowhy.utils.ordered_set import OrderedSet
[docs]def adjacency_matrix_to_adjacency_list(adjacency_matrix, labels=None):
"""
Convert the adjacency matrix of a graph to an adjacency list.
:param adjacency_matrix: A numpy array representing the graph adjacency matrix.
:param labels: List of labels.
:returns: Adjacency list as a dictionary.
"""
adjlist = dict()
if labels is None:
labels = [str(i + 1) for i in range(adjacency_matrix.shape[0])]
for i in range(adjacency_matrix.shape[0]):
adjlist[labels[i]] = list()
for j in range(adjacency_matrix.shape[1]):
if adjacency_matrix[i, j] != 0:
adjlist[labels[i]].append(labels[j])
return adjlist
[docs]def adjacency_matrix_to_graph(adjacency_matrix, labels=None):
"""
Convert a given graph adjacency matrix to DOT format.
:param adjacency_matrix: A numpy array representing the graph adjacency matrix.
:param labels: List of labels.
:returns: Graph in DOT format.
"""
# Only consider edges have absolute edge weight > 0.01
idx = np.abs(adjacency_matrix) > 0.01
dirs = np.where(idx)
import graphviz
d = graphviz.Digraph(engine="dot")
names = labels if labels else [f"x{i}" for i in range(len(adjacency_matrix))]
for name in names:
d.node(name)
for to, from_, coef in zip(dirs[0], dirs[1], adjacency_matrix[idx]):
d.edge(names[from_], names[to], label=str(coef))
return d
[docs]def str_to_dot(string):
"""
Converts input string from graphviz library to valid DOT graph format.
:param string: Graph in DOT format.
:returns: DOT string converted to a suitable format for the DoWhy library.
"""
graph = string.strip().replace("\n", ";").replace("\t", "")
graph = graph[:9] + graph[10:-2] + graph[-1] # Removing unnecessary characters from string
return graph
[docs]def find_ancestor(node_set, node_names, adjacency_matrix, node2idx, idx2node):
"""
Finds ancestors of a given set of nodes in a given graph.
:param node_set: Set of nodes whos ancestors must be obtained.
:param node_names: Name of all nodes in the graph.
:param adjacency_matrix: Graph adjacency matrix.
:param node2idx: A dictionary mapping node names to their row or column index in the adjacency matrix.
:param idx2node: A dictionary mapping the row or column indices in the adjacency matrix to the corresponding node names.
:returns: OrderedSet containing ancestors of all nodes in the node_set.
"""
def find_ancestor_help(node_name, node_names, adjacency_matrix, node2idx, idx2node):
ancestors = OrderedSet()
nodes_to_visit = LifoQueue(maxsize=len(node_names))
nodes_to_visit.put(node2idx[node_name])
while not nodes_to_visit.empty():
child = nodes_to_visit.get()
ancestors.add(idx2node[child])
for i in range(len(node_names)):
if (
idx2node[i] not in ancestors and adjacency_matrix[i, child] == 1
): # For edge a->b, a is along height and b is along width of adjacency matrix
nodes_to_visit.put(i)
return ancestors
ancestors = OrderedSet()
for node_name in node_set.get_all():
ancestors = ancestors.union(find_ancestor_help(node_name, node_names, adjacency_matrix, node2idx, idx2node))
return ancestors
[docs]def induced_graph(node_set, adjacency_matrix, node2idx):
"""
To obtain the induced graph corresponding to a subset of nodes.
:param node_set: Set of nodes whos ancestors must be obtained.
:param adjacency_matrix: Graph adjacency matrix.
:param node2idx: A dictionary mapping node names to their row or column index in the adjacency matrix.
:returns: Numpy array representing the adjacency matrix of the induced graph.
"""
node_idx_list = [node2idx[node] for node in node_set]
node_idx_list.sort()
adjacency_matrix_induced = adjacency_matrix.copy()
adjacency_matrix_induced = adjacency_matrix_induced[node_idx_list]
adjacency_matrix_induced = adjacency_matrix_induced[:, node_idx_list]
return adjacency_matrix_induced
[docs]def find_c_components(adjacency_matrix, node_set, idx2node):
"""
Obtain C-components in a graph.
:param adjacency_matrix: Graph adjacency matrix.
:param node_set: Set of nodes whos ancestors must be obtained.
:param idx2node: A dictionary mapping the row or column indices in the adjacency matrix to the corresponding node names.
:returns: List of C-components in the graph.
"""
num_nodes = len(node_set)
adj_matrix = adjacency_matrix.copy()
adjacency_list = [[] for _ in range(num_nodes)]
# Modify graph such that it only contains bidirected edges
for h in range(0, num_nodes - 1):
for w in range(h + 1, num_nodes):
if adjacency_matrix[h, w] == 1 and adjacency_matrix[w, h] == 1:
adjacency_list[h].append(w)
adjacency_list[w].append(h)
else:
adj_matrix[h, w] = 0
adj_matrix[w, h] = 0
# Find c components by finding connected components on the undirected graph
visited = [False for _ in range(num_nodes)]
def dfs(node_idx, component):
visited[node_idx] = True
component.add(idx2node[node_idx])
for neighbour in adjacency_list[node_idx]:
if visited[neighbour] == False:
dfs(neighbour, component)
c_components = []
for i in range(num_nodes):
if visited[i] == False:
component = OrderedSet()
dfs(i, component)
c_components.append(component)
return c_components
[docs]def daggity_to_dot(daggity_string):
"""
Converts the input daggity_string to valid DOT graph format.
:param daggity_string: Output graph from Daggity site
:returns: DOT string
"""
graph = re.sub(r"\n", "; ", daggity_string)
graph = re.sub(r"^dag ", "digraph ", graph)
graph = re.sub("{;", "{", graph)
graph = re.sub("};", "}", graph)
graph = re.sub("outcome,*,", "", graph)
graph = re.sub("adjusted,*", "", graph)
graph = re.sub("exposure,*", "", graph)
graph = re.sub("latent,*", 'observed="no",', graph)
graph = re.sub(",]", "]", graph)
return graph
[docs]def get_simple_ordered_tree(n):
"""
Generates a simple-ordered tree. The tree is just a
directed acyclic graph of n nodes with the structure
0 --> 1 --> .... --> n.
"""
g = nx.DiGraph()
for i in range(n):
g.add_node(i)
for i in range(n - 1):
g.add_edges_from([(i, i + 1, {})])
return g
[docs]def is_connected(g):
"""
Checks if a the directed acyclic graph is connected.
"""
u = convert_to_undirected_graph(g)
return nx.is_connected(u)
[docs]def convert_to_undirected_graph(g):
u = nx.Graph()
for n in g.nodes:
u.add_node(n)
for e in g.edges:
u.add_edges_from([(e[0], e[1], {})])
return u
[docs]def get_random_node_pair(n):
"""
Randomly generates a pair of nodes.
"""
i = np.random.randint(0, n)
j = i
while j == i:
j = np.random.randint(0, n)
return i, j
[docs]def find_predecessor(i, j, g):
"""
Finds a predecessor, k, in the path between two nodes, i and j,
in the graph, g.
"""
parents = list(g.predecessors(j))
u = convert_to_undirected_graph(g)
for pa in parents:
try:
path = shortest_path(u, pa, i)
return pa
except:
pass
return None
[docs]def del_edge(i, j, g):
"""
Deletes the edge i --> j in the graph, g. The edge is only
deleted if this removal does NOT cause the graph to be
disconnected.
"""
if g.has_edge(i, j) is True:
g.remove_edge(i, j)
if is_connected(g) is False:
g.add_edges_from([(i, j, {})])
[docs]def add_edge(i, j, g):
"""
Adds an edge i --> j to the graph, g. The edge is only
added if this addition does NOT cause the graph to have
cycles.
"""
g.add_edges_from([(i, j, {})])
if is_directed_acyclic_graph(g) is False:
g.remove_edge(i, j)