graphkit-learn/gklearn/preimage/median_graph_estimator.py

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Mar 16 18:04:55 2020

@author: ljia
"""
import numpy as np
from gklearn.preimage.common_types import AlgorithmState
from gklearn.preimage import misc
from gklearn.preimage.timer import Timer
from gklearn.utils.utils import graph_isIdentical
import time
from tqdm import tqdm
import sys
import networkx as nx


class MedianGraphEstimator(object):
	
	def __init__(self, ged_env, constant_node_costs):
		"""Constructor.
		
		Parameters
		----------
		ged_env : gklearn.gedlib.gedlibpy.GEDEnv
			Initialized GED environment. The edit costs must be set by the user.
			
		constant_node_costs : Boolean
			Set to True if the node relabeling costs are constant.
		"""
		self.__ged_env = ged_env
		self.__init_method = 'BRANCH_FAST'
		self.__init_options = ''
		self.__descent_method = 'BRANCH_FAST'
		self.__descent_options = ''
		self.__refine_method = 'IPFP'
		self.__refine_options = ''
		self.__constant_node_costs = constant_node_costs
		self.__labeled_nodes = (ged_env.get_num_node_labels() > 1)
		self.__node_del_cost = ged_env.get_node_del_cost(ged_env.get_node_label(1))
		self.__node_ins_cost = ged_env.get_node_ins_cost(ged_env.get_node_label(1))
		self.__labeled_edges = (ged_env.get_num_edge_labels() > 1)
		self.__edge_del_cost = ged_env.get_edge_del_cost(ged_env.get_edge_label(1))
		self.__edge_ins_cost = ged_env.get_edge_ins_cost(ged_env.get_edge_label(1))
		self.__init_type = 'RANDOM'
		self.__num_random_inits = 10
		self.__desired_num_random_inits = 10
		self.__use_real_randomness = True
		self.__seed = 0
		self.__refine = True
		self.__time_limit_in_sec = 0
		self.__epsilon = 0.0001
		self.__max_itrs = 100
		self.__max_itrs_without_update = 3
		self.__num_inits_increase_order = 10
		self.__init_type_increase_order = 'K-MEANS++'
		self.__max_itrs_increase_order = 10
		self.__print_to_stdout = 2
		self.__median_id = np.inf # @todo: check
		self.__median_node_id_prefix = '' # @todo: check
		self.__node_maps_from_median = {}
		self.__sum_of_distances = 0
		self.__best_init_sum_of_distances = np.inf
		self.__converged_sum_of_distances = np.inf
		self.__runtime = None
		self.__runtime_initialized = None
		self.__runtime_converged = None
		self.__itrs = [] # @todo: check: {} ?
		self.__num_decrease_order = 0
		self.__num_increase_order = 0
		self.__num_converged_descents = 0
		self.__state = AlgorithmState.TERMINATED
		
		if ged_env is None:
			raise Exception('The GED environment pointer passed to the constructor of MedianGraphEstimator is null.')
		elif not ged_env.is_initialized():
			raise Exception('The GED environment is uninitialized. Call gedlibpy.GEDEnv.init() before passing it to the constructor of MedianGraphEstimator.')
	
	
	def set_options(self, options):
		"""Sets the options of the estimator.

		Parameters
		----------
		options : string
			String that specifies with which options to run the estimator.
		"""
		self.__set_default_options()
		options_map = misc.options_string_to_options_map(options)
		for opt_name, opt_val in options_map.items():
			if opt_name == 'init-type':
				self.__init_type = opt_val
				if opt_val != 'MEDOID' and opt_val != 'RANDOM' and opt_val != 'MIN' and opt_val != 'MAX' and opt_val != 'MEAN':
					raise Exception('Invalid argument ' + opt_val + ' for option init-type. Usage: options = "[--init-type RANDOM|MEDOID|EMPTY|MIN|MAX|MEAN] [...]"')
			elif opt_name == 'random-inits':
				try:
					self.__num_random_inits = int(opt_val)
					self.__desired_num_random_inits = self.__num_random_inits
				except:
					raise Exception('Invalid argument "' + opt_val + '" for option random-inits. Usage: options = "[--random-inits <convertible to int greater 0>]"')

				if self.__num_random_inits <= 0:
					raise Exception('Invalid argument "' + opt_val + '" for option random-inits. Usage: options = "[--random-inits <convertible to int greater 0>]"')
	
			elif opt_name == 'randomness':
				if opt_val == 'PSEUDO':
					self.__use_real_randomness = False
	
				elif opt_val == 'REAL':
					self.__use_real_randomness = True
	
				else:
					raise Exception('Invalid argument "' + opt_val  + '" for option randomness. Usage: options = "[--randomness REAL|PSEUDO] [...]"')
	
			elif opt_name == 'stdout':
				if opt_val == '0':
					self.__print_to_stdout = 0
	
				elif opt_val == '1':
					self.__print_to_stdout = 1
	
				elif opt_val == '2':
					self.__print_to_stdout = 2
	
				else:
					raise Exception('Invalid argument "' + opt_val  + '" for option stdout. Usage: options = "[--stdout 0|1|2] [...]"')
	
			elif opt_name == 'refine':
				if opt_val == 'TRUE':
					self.__refine = True
	
				elif opt_val == 'FALSE':
					self.__refine = False
	
				else:
					raise Exception('Invalid argument "' + opt_val  + '" for option refine. Usage: options = "[--refine TRUE|FALSE] [...]"')
	
			elif opt_name == 'time-limit':
				try:
					self.__time_limit_in_sec = float(opt_val)
	
				except:
					raise Exception('Invalid argument "' + opt_val + '" for option time-limit.  Usage: options = "[--time-limit <convertible to double>] [...]')
	
			elif opt_name == 'max-itrs':
				try:
					self.__max_itrs = int(opt_val)
	
				except:
					raise Exception('Invalid argument "' + opt_val + '" for option max-itrs. Usage: options = "[--max-itrs <convertible to int>] [...]')
	
			elif opt_name == 'max-itrs-without-update':
				try:
					self.__max_itrs_without_update = int(opt_val)
	
				except:
					raise Exception('Invalid argument "' + opt_val + '" for option max-itrs-without-update. Usage: options = "[--max-itrs-without-update <convertible to int>] [...]')
	
			elif opt_name == 'seed':
				try:
					self.__seed = int(opt_val)
	
				except:
					raise Exception('Invalid argument "' + opt_val + '" for option seed. Usage: options = "[--seed <convertible to int greater equal 0>] [...]')
	
			elif opt_name == 'epsilon':
				try:
					self.__epsilon = float(opt_val)
	
				except:
					raise Exception('Invalid argument "' + opt_val + '" for option epsilon. Usage: options = "[--epsilon <convertible to double greater 0>] [...]')
	
				if self.__epsilon <= 0:
					raise Exception('Invalid argument "' + opt_val + '" for option epsilon. Usage: options = "[--epsilon <convertible to double greater 0>] [...]')
	
			elif opt_name == 'inits-increase-order':
				try:
					self.__num_inits_increase_order = int(opt_val)
	
				except:
					raise Exception('Invalid argument "' + opt_val + '" for option inits-increase-order. Usage: options = "[--inits-increase-order <convertible to int greater 0>]"')
	
				if self.__num_inits_increase_order <= 0:
					raise Exception('Invalid argument "' + opt_val + '" for option inits-increase-order. Usage: options = "[--inits-increase-order <convertible to int greater 0>]"')

			elif opt_name == 'init-type-increase-order':
				self.__init_type_increase_order = opt_val
				if opt_val != 'CLUSTERS' and opt_val != 'K-MEANS++':
					raise Exception('Invalid argument ' + opt_val + ' for option init-type-increase-order. Usage: options = "[--init-type-increase-order CLUSTERS|K-MEANS++] [...]"')
	
			elif opt_name == 'max-itrs-increase-order':
				try:
					self.__max_itrs_increase_order = int(opt_val)
	
				except:
					raise Exception('Invalid argument "' + opt_val + '" for option max-itrs-increase-order. Usage: options = "[--max-itrs-increase-order <convertible to int>] [...]')

			else:
				valid_options = '[--init-type <arg>] [--random-inits <arg>] [--randomness <arg>] [--seed <arg>] [--stdout <arg>] '
				valid_options += '[--time-limit <arg>] [--max-itrs <arg>] [--epsilon <arg>] '
				valid_options += '[--inits-increase-order <arg>] [--init-type-increase-order <arg>] [--max-itrs-increase-order <arg>]'
				raise Exception('Invalid option "' + opt_name + '". Usage: options = "' + valid_options + '"')
 
		
	def set_init_method(self, init_method, init_options=''):
		"""Selects method to be used for computing the initial medoid graph.
		
		Parameters
		----------
		init_method : string
			The selected method. Default: ged::Options::GEDMethod::BRANCH_UNIFORM.
		
		init_options : string
			The options for the selected method. Default: "".
		
		Notes
		-----
		Has no effect unless "--init-type MEDOID" is passed to set_options().
		"""
		self.__init_method = init_method;
		self.__init_options = init_options;
	
	
	def set_descent_method(self, descent_method, descent_options=''):
		"""Selects method to be used for block gradient descent..
		
		Parameters
		----------
		descent_method : string
			The selected method. Default: ged::Options::GEDMethod::BRANCH_FAST.
		
		descent_options : string
			The options for the selected method. Default: "".
		
		Notes
		-----
		Has no effect unless "--init-type MEDOID" is passed to set_options().
		"""
		self.__descent_method = descent_method;
		self.__descent_options = descent_options;

	
	def set_refine_method(self, refine_method, refine_options):
		"""Selects method to be used for improving the sum of distances and the node maps for the converged median.
		
		Parameters
		----------
		refine_method : string
			The selected method. Default: "IPFP".
			
		refine_options : string 
			The options for the selected method. Default: "".
					
		Notes
		-----
		Has no effect if "--refine FALSE" is passed to set_options().
		"""
		self.__refine_method = refine_method
		self.__refine_options = refine_options

	
	def run(self, graph_ids, set_median_id, gen_median_id):
		"""Computes a generalized median graph.
		
		Parameters
		----------
		graph_ids : list[integer]
			The IDs of the graphs for which the median should be computed. Must have been added to the environment passed to the constructor.
		
		set_median_id : integer
			The ID of the computed set-median. A dummy graph with this ID must have been added to the environment passed to the constructor. Upon termination, the computed median can be obtained via gklearn.gedlib.gedlibpy.GEDEnv.get_graph().


		gen_median_id : integer
			The ID of the computed generalized median. Upon termination, the computed median can be obtained via gklearn.gedlib.gedlibpy.GEDEnv.get_graph().
		"""
		# Sanity checks.
		if len(graph_ids) == 0:
			raise Exception('Empty vector of graph IDs, unable to compute median.')
		all_graphs_empty = True
		for graph_id in graph_ids:
			if self.__ged_env.get_graph_num_nodes(graph_id) > 0:
				self.__median_node_id_prefix = self.__ged_env.get_original_node_ids(graph_id)[0]
				all_graphs_empty = False
				break
		if all_graphs_empty:
			raise Exception('All graphs in the collection are empty.')
			
		# Start timer and record start time.
		start = time.time()
		timer = Timer(self.__time_limit_in_sec)
		self.__median_id = gen_median_id
		self.__state = AlgorithmState.TERMINATED
		
		# Get ExchangeGraph representations of the input graphs.
		graphs = {}
		for graph_id in graph_ids:
			# @todo: get_nx_graph() function may need to be modified according to the coming code.
			graphs[graph_id] = self.__ged_env.get_nx_graph(graph_id, True, True, False)
# 		print(self.__ged_env.get_graph_internal_id(0))
# 		print(graphs[0].graph)
# 		print(graphs[0].nodes(data=True))
# 		print(graphs[0].edges(data=True))
# 		print(nx.adjacency_matrix(graphs[0]))

			
		# Construct initial medians.
		medians = []
		self.__construct_initial_medians(graph_ids, timer, medians)
		end_init = time.time()
		self.__runtime_initialized = end_init - start
# 		print(medians[0].graph)
# 		print(medians[0].nodes(data=True))
# 		print(medians[0].edges(data=True))
# 		print(nx.adjacency_matrix(medians[0]))
		
		# Reset information about iterations and number of times the median decreases and increases.
		self.__itrs = [0] * len(medians)
		self.__num_decrease_order = 0
		self.__num_increase_order = 0
		self.__num_converged_descents = 0
		
		# Initialize the best median.
		best_sum_of_distances = np.inf
		self.__best_init_sum_of_distances = np.inf
		node_maps_from_best_median = {}
		
		# Run block gradient descent from all initial medians.
		self.__ged_env.set_method(self.__descent_method, self.__descent_options)
		for median_pos in range(0, len(medians)):
			
			# Terminate if the timer has expired and at least one SOD has been computed.
			if timer.expired() and median_pos > 0:
				break
			
			# Print information about current iteration.
			if self.__print_to_stdout == 2:
				print('\n===========================================================')
				print('Block gradient descent for initial median', str(median_pos + 1), 'of', str(len(medians)), '.')
				print('-----------------------------------------------------------')
				
			# Get reference to the median.
			median = medians[median_pos]
			
			# Load initial median into the environment.
			self.__ged_env.load_nx_graph(median, gen_median_id)
			self.__ged_env.init(self.__ged_env.get_init_type())
			
			# Print information about current iteration.
			if self.__print_to_stdout == 2:
				progress = tqdm(desc='\rComputing initial node maps', total=len(graph_ids), file=sys.stdout)
				
			# Compute node maps and sum of distances for initial median.
			self.__sum_of_distances = 0
			self.__node_maps_from_median.clear() # @todo
			for graph_id in graph_ids:
				self.__ged_env.run_method(gen_median_id, graph_id)
				self.__node_maps_from_median[graph_id] = self.__ged_env.get_node_map(gen_median_id, graph_id)
# 				print(self.__node_maps_from_median[graph_id])
				self.__sum_of_distances += self.__ged_env.get_induced_cost(gen_median_id, graph_id) # @todo: the C++ implementation for this function in GedLibBind.ipp re-call get_node_map() once more, this is not neccessary.
# 				print(self.__sum_of_distances)
				# Print information about current iteration.
				if self.__print_to_stdout == 2:
					progress.update(1)
					
			self.__best_init_sum_of_distances = min(self.__best_init_sum_of_distances, self.__sum_of_distances)
			self.__ged_env.load_nx_graph(median, set_median_id)
# 			print(self.__best_init_sum_of_distances)
			
			# Print information about current iteration.
			if self.__print_to_stdout == 2:
				print('\n')
				
			# Run block gradient descent from initial median.
			converged = False
			itrs_without_update = 0
			while not self.__termination_criterion_met(converged, timer, self.__itrs[median_pos], itrs_without_update):
				
				# Print information about current iteration.
				if self.__print_to_stdout == 2:
					print('\n===========================================================')
					print('Iteration', str(self.__itrs[median_pos] + 1), 'for initial median', str(median_pos + 1), 'of', str(len(medians)), '.')
					print('-----------------------------------------------------------')
					
				# Initialize flags that tell us what happened in the iteration.
				median_modified = False
				node_maps_modified = False
				decreased_order = False
				increased_order = False
				
				# Update the median. # @todo!!!!!!!!!!!!!!!!!!!!!!
				median_modified = self.__update_median(graphs, median)
				if not median_modified or self.__itrs[median_pos] == 0:
					decreased_order = False
					if not decreased_order or self.__itrs[median_pos] == 0:
						increased_order = False
						
				# Update the number of iterations without update of the median.
				if median_modified or decreased_order or increased_order:
					itrs_without_update = 0
				else:
					itrs_without_update += 1
					
				# Print information about current iteration.
				if self.__print_to_stdout == 2:
					print('Loading median to environment: ... ', end='')
					
				# Load the median into the environment.
				# @todo: should this function use the original node label?
				self.__ged_env.load_nx_graph(median, gen_median_id)
				self.__ged_env.init(self.__ged_env.get_init_type())
					
				# Print information about current iteration.
				if self.__print_to_stdout == 2:
					print('done.')					
					
				# Print information about current iteration.
				if self.__print_to_stdout == 2:
					print('Updating induced costs: ... ', end='')

				# Compute induced costs of the old node maps w.r.t. the updated median.
				for graph_id in graph_ids:
# 					print(self.__ged_env.get_induced_cost(gen_median_id, graph_id))
					# @todo: watch out if compute_induced_cost is correct, this may influence: increase/decrease order, induced_cost() in the following code.!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
					self.__ged_env.compute_induced_cost(gen_median_id, graph_id)
# 					print('---------------------------------------')
# 					print(self.__ged_env.get_induced_cost(gen_median_id, graph_id))
					
				# Print information about current iteration.
				if self.__print_to_stdout == 2:
					print('done.')					
					
				# Update the node maps.
				node_maps_modified = self.__update_node_maps() # @todo

				# Update the order of the median if no improvement can be found with the current order.
				
				# Update the sum of distances.
				old_sum_of_distances = self.__sum_of_distances
				self.__sum_of_distances = 0
				for graph_id in self.__node_maps_from_median:
					self.__sum_of_distances += self.__ged_env.get_induced_cost(gen_median_id, graph_id) # @todo: see above.
					
				# Print information about current iteration.
				if self.__print_to_stdout == 2:
					print('Old local SOD: ', old_sum_of_distances)
					print('New local SOD: ', self.__sum_of_distances)
					print('Best converged SOD: ', best_sum_of_distances)
					print('Modified median: ', median_modified)
					print('Modified node maps: ', node_maps_modified)
					print('Decreased order: ', decreased_order)
					print('Increased order: ', increased_order)
					print('===========================================================\n')
					
				converged = not (median_modified or node_maps_modified or decreased_order or increased_order)
				
				self.__itrs[median_pos] += 1
				
			# Update the best median.
			if self.__sum_of_distances < self.__best_init_sum_of_distances:
				best_sum_of_distances = self.__sum_of_distances
				node_maps_from_best_median = self.__node_maps_from_median
				best_median = median
				
			# Update the number of converged descents.
			if converged:
				self.__num_converged_descents += 1
				
		# Store the best encountered median.
		self.__sum_of_distances = best_sum_of_distances
		self.__node_maps_from_median = node_maps_from_best_median
		self.__ged_env.load_nx_graph(best_median, gen_median_id)
		self.__ged_env.init(self.__ged_env.get_init_type())
		end_descent = time.time()
		self.__runtime_converged = end_descent - start
		
		# Refine the sum of distances and the node maps for the converged median.
		self.__converged_sum_of_distances = self.__sum_of_distances
		if self.__refine:
			self.__improve_sum_of_distances(timer) # @todo
		
		# Record end time, set runtime and reset the number of initial medians.
		end = time.time()
		self.__runtime = end - start
		self.__num_random_inits = self.__desired_num_random_inits
		
		# Print global information.
		if self.__print_to_stdout != 0:
			print('\n===========================================================')
			print('Finished computation of generalized median graph.')
			print('-----------------------------------------------------------')
			print('Best SOD after initialization: ', self.__best_init_sum_of_distances)
			print('Converged SOD: ', self.__converged_sum_of_distances)
			if self.__refine:
				print('Refined SOD: ', self.__sum_of_distances)
			print('Overall runtime: ', self.__runtime)
			print('Runtime of initialization: ', self.__runtime_initialized)
			print('Runtime of block gradient descent: ', self.__runtime_converged - self.__runtime_initialized)
			if self.__refine:
				print('Runtime of refinement: ', self.__runtime - self.__runtime_converged)
			print('Number of initial medians: ', len(medians))
			total_itr = 0
			num_started_descents = 0
			for itr in self.__itrs:
				total_itr += itr
				if itr > 0:
					num_started_descents += 1
			print('Size of graph collection: ', len(graph_ids))
			print('Number of started descents: ', num_started_descents)
			print('Number of converged descents: ', self.__num_converged_descents)
			print('Overall number of iterations: ', total_itr)
			print('Overall number of times the order decreased: ', self.__num_decrease_order)
			print('Overall number of times the order increased: ', self.__num_increase_order)
			print('===========================================================\n')
	
	
	def get_sum_of_distances(self, state=''):
		"""Returns the sum of distances.
		
		Parameters
		----------
		state : string
			The state of the estimator. Can be 'initialized' or 'converged'. Default: ""
			
		Returns
		-------
		float
			The sum of distances (SOD) of the median when the estimator was in the state `state` during the last call to run(). If `state` is not given, the converged SOD (without refinement) or refined SOD (with refinement) is returned.
		"""
		if not self.__median_available():
			raise Exception('No median has been computed. Call run() before calling get_sum_of_distances().')
		if state == 'initialized':
			return self.__best_init_sum_of_distances
		if state == 'converged':
			return self.__converged_sum_of_distances
		return self.__sum_of_distances
	
	
	def __set_default_options(self):
		self.__init_type = 'RANDOM'
		self.__num_random_inits = 10
		self.__desired_num_random_inits = 10
		self.__use_real_randomness = True
		self.__seed = 0
		self.__refine = True
		self.__time_limit_in_sec = 0
		self.__epsilon = 0.0001
		self.__max_itrs = 100
		self.__max_itrs_without_update = 3
		self.__num_inits_increase_order = 10
		self.__init_type_increase_order = 'K-MEANS++'
		self.__max_itrs_increase_order = 10
		self.__print_to_stdout = 2
		
		
	def __construct_initial_medians(self, graph_ids, timer, initial_medians):
		# Print information about current iteration.
		if self.__print_to_stdout == 2:
			print('\n===========================================================')
			print('Constructing initial median(s).')
			print('-----------------------------------------------------------')
			
		# Compute or sample the initial median(s).
		initial_medians.clear()
		if self.__init_type == 'MEDOID':
			self.__compute_medoid(graph_ids, timer, initial_medians)
		elif self.__init_type == 'MAX':
			pass # @todo
# 			compute_max_order_graph_(graph_ids, initial_medians)
		elif self.__init_type == 'MIN':
			pass # @todo
# 			compute_min_order_graph_(graph_ids, initial_medians)
		elif self.__init_type == 'MEAN':
			pass # @todo
# 			compute_mean_order_graph_(graph_ids, initial_medians)
		else:
			pass # @todo
# 			sample_initial_medians_(graph_ids, initial_medians)

		# Print information about current iteration.
		if self.__print_to_stdout == 2:
			print('===========================================================')
			
			
	def __compute_medoid(self, graph_ids, timer, initial_medians):
		# Use method selected for initialization phase.
		self.__ged_env.set_method(self.__init_method, self.__init_options)
		
		# Print information about current iteration.
		if self.__print_to_stdout == 2:
			progress = tqdm(desc='\rComputing medoid', total=len(graph_ids), file=sys.stdout)
			
		# Compute the medoid.
		medoid_id = graph_ids[0]
		best_sum_of_distances = np.inf
		for g_id in graph_ids:
			if timer.expired():
				self.__state = AlgorithmState.CALLED
				break
			sum_of_distances = 0
			for h_id in graph_ids:
				self.__ged_env.run_method(g_id, h_id)
				sum_of_distances += self.__ged_env.get_upper_bound(g_id, h_id)
			if sum_of_distances < best_sum_of_distances:
				best_sum_of_distances = sum_of_distances
				medoid_id = g_id
				
			# Print information about current iteration.
			if self.__print_to_stdout == 2:
				progress.update(1)
		initial_medians.append(self.__ged_env.get_nx_graph(medoid_id, True, True, False)) # @todo
		
		# Print information about current iteration.
		if self.__print_to_stdout == 2:
			print('\n')
			
		
	def __termination_criterion_met(self, converged, timer, itr, itrs_without_update):
		if timer.expired() or (itr >= self.__max_itrs if self.__max_itrs >= 0 else False):
			if self.__state == AlgorithmState.TERMINATED:
				self.__state = AlgorithmState.INITIALIZED
			return True
		return converged or (itrs_without_update > self.__max_itrs_without_update if self.__max_itrs_without_update >= 0 else False)
	
	
	def __update_median(self, graphs, median):
		# Print information about current iteration.
		if self.__print_to_stdout == 2:
			print('Updating median: ', end='')
			
		# Store copy of the old median.
		old_median = median.copy() # @todo: this is just a shallow copy.
		
		# Update the node labels.
		if self.__labeled_nodes:
			self.__update_node_labels(graphs, median)
			
		# Update the edges and their labels.
		self.__update_edges(graphs, median)
		
		# Print information about current iteration.
		if self.__print_to_stdout == 2:
			print('done.')
			
		return not self.__are_graphs_equal(median, old_median)
		
		
	def __update_node_labels(self, graphs, median):
		
		# Print information about current iteration.
		if self.__print_to_stdout == 2:
			print('nodes ... ', end='')
			
		# Iterate through all nodes of the median.
		for i in range(0, nx.number_of_nodes(median)):
# 			print('i: ', i)
			# Collect the labels of the substituted nodes.
			node_labels = []
			for graph_id, graph in graphs.items():
# 				print('graph_id: ', graph_id)
# 				print(self.__node_maps_from_median[graph_id])
				k = self.__get_node_image_from_map(self.__node_maps_from_median[graph_id], i)
# 				print('k: ', k)
				if k != np.inf:
					node_labels.append(graph.nodes[k])
					
			# Compute the median label and update the median.
			if len(node_labels) > 0:
				median_label = self.__ged_env.get_median_node_label(node_labels)
				if self.__ged_env.get_node_rel_cost(median.nodes[i], median_label) > self.__epsilon:
					nx.set_node_attributes(median, {i: median_label})
					
					
	def __update_edges(self, graphs, median):
		# Print information about current iteration.
		if self.__print_to_stdout == 2:
			print('edges ... ', end='')
			
		# Clear the adjacency lists of the median and reset number of edges to 0.
		median_edges = list(median.edges)		
		for (head, tail) in median_edges:
			median.remove_edge(head, tail)
		
		# @todo: what if edge is not labeled?
		# Iterate through all possible edges (i,j) of the median.
		for i in range(0, nx.number_of_nodes(median)):
			for j in range(i + 1, nx.number_of_nodes(median)):
				
				# Collect the labels of the edges to which (i,j) is mapped by the node maps.
				edge_labels = []
				for graph_id, graph in graphs.items():
					k = self.__get_node_image_from_map(self.__node_maps_from_median[graph_id], i)
					l = self.__get_node_image_from_map(self.__node_maps_from_median[graph_id], j)
					if k != np.inf and l != np.inf:
						if graph.has_edge(k, l):
							edge_labels.append(graph.edges[(k, l)])
							
				# Compute the median edge label and the overall edge relabeling cost.
				rel_cost = 0
				median_label = self.__ged_env.get_edge_label(1)
				if median.has_edge(i, j):
					median_label = median.edges[(i, j)]
				if self.__labeled_edges and len(edge_labels) > 0:
					new_median_label = self.__ged_env.median_edge_label(edge_labels)
					if self.__ged_env.get_edge_rel_cost(median_label, new_median_label) > self.__epsilon:
						median_label = new_median_label
					for edge_label in edge_labels:
						rel_cost += self.__ged_env.get_edge_rel_cost(median_label, edge_label)
						
				# Update the median.
				if rel_cost < (self.__edge_ins_cost + self.__edge_del_cost) * len(edge_labels) - self.__edge_del_cost * len(graphs):
					median.add_edge(i, j, **median_label)
				else:
					if median.has_edge(i, j):
						median.remove_edge(i, j)


	def __update_node_maps(self):
		# Print information about current iteration.
		if self.__print_to_stdout == 2:
			progress = tqdm(desc='\rUpdating node maps', total=len(self.__node_maps_from_median), file=sys.stdout)
			
		# Update the node maps.
		node_maps_were_modified = False
		for graph_id in self.__node_maps_from_median:
			self.__ged_env.run_method(self.__median_id, graph_id)
			if self.__ged_env.get_upper_bound(self.__median_id, graph_id) < self.__ged_env.get_induced_cost(self.__median_id, graph_id) - self.__epsilon: # @todo: see above.
				self.__node_maps_from_median[graph_id] = self.__ged_env.get_node_map(self.__median_id, graph_id) # @todo: node_map may not assigned.
				node_maps_were_modified = True
			# Print information about current iteration.
			if self.__print_to_stdout == 2:
				progress.update(1)
			
		# Print information about current iteration.
		if self.__print_to_stdout == 2:
			print('\n')
			
		# Return true if the node maps were modified.
		return node_maps_were_modified
	
	
	def __improve_sum_of_distances(self, timer):
		pass
	
	
	def __median_available(self):
		return self.__median_id != np.inf
		
				
	def __get_node_image_from_map(self, node_map, node):
		"""
		Return ID of the node mapping of `node` in `node_map`.

		Parameters
		----------
		node_map : list[tuple(int, int)]
			List of node maps where the mapping node is found.
		
		node : int
			The mapping node of this node is returned

		Raises
		------
		Exception
			If the node with ID `node` is not contained in the source nodes of the node map.

		Returns
		-------
		int
			ID of the mapping of `node`.
			
		Notes
		-----
		This function is not implemented in the `ged::MedianGraphEstimator` class of the `GEDLIB` library. Instead it is a Python implementation of the `ged::NodeMap::image` function.
		"""
		if node < len(node_map):
			return node_map[node][1] if node_map[node][1] < len(node_map) else np.inf
		else:
 			raise Exception('The node with ID ', str(node), ' is not contained in the source nodes of the node map.')
		return np.inf
				
	
	def __are_graphs_equal(self, g1, g2):
		"""
		Check if the two graphs are equal.

		Parameters
		----------
		g1 : NetworkX graph object
			Graph 1 to be compared.
		
		g2 : NetworkX graph object
			Graph 2 to be compared.

		Returns
		-------
		bool
			True if the two graph are equal.
			
		Notes
		-----
		This is not an identical check. Here the two graphs are equal if and only if their original_node_ids, nodes, all node labels, edges and all edge labels are equal. This function is specifically designed for class `MedianGraphEstimator` and should not be used elsewhere.
		"""
		# check original node ids.
		if not g1.graph['original_node_ids'] == g2.graph['original_node_ids']:
			return False
		# check nodes.
		nlist1 = [n for n in g1.nodes(data=True)]
		nlist2 = [n for n in g2.nodes(data=True)]
		if not nlist1 == nlist2:
			return False
		# check edges.
		elist1 = [n for n in g1.edges(data=True)]
		elist2 = [n for n in g2.edges(data=True)]
		if not elist1 == elist2:
			return False

		return True
	
	
	def compute_my_cost(g, h, node_map):
		cost = 0.0
		for node in g.nodes:
			cost += 0