OpenI
/
graphkit-learn

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Fri Apr 26 11:49:12 2019

Iterative alternate minimizations using GED.
@author: ljia
"""
import numpy as np
import random
import networkx as nx

import sys
#from Cython_GedLib_2 import librariesImport, script
import librariesImport, script
sys.path.insert(0, "../")
from pygraph.utils.graphfiles import saveDataset
from pygraph.utils.graphdataset import get_dataset_attributes
from pygraph.utils.utils import graph_isIdentical, get_node_labels, get_edge_labels
#from pygraph.utils.utils import graph_deepcopy


def iam(Gn, c_ei=3, c_er=3, c_es=1, node_label='atom', edge_label='bond_type', 
        connected=True):
    """See my name, then you know what I do.
    """
#    Gn = Gn[0:10]
    Gn = [nx.convert_node_labels_to_integers(g) for g in Gn]
    
    # phase 1: initilize.
    # compute set-median.
    dis_min = np.inf
    pi_p = []
    pi_all = []
    for idx1, G_p in enumerate(Gn):
        dist_sum = 0
        pi_all.append([])
        for idx2, G_p_prime in enumerate(Gn):
            dist_tmp, pi_tmp, _ = GED(G_p, G_p_prime)
            pi_all[idx1].append(pi_tmp)
            dist_sum += dist_tmp
        if dist_sum < dis_min:
            dis_min = dist_sum
            G = G_p.copy()
            idx_min = idx1
    # list of edit operations.        
    pi_p = pi_all[idx_min]
            
    # phase 2: iteration.
    ds_attrs = get_dataset_attributes(Gn, attr_names=['edge_labeled', 'node_attr_dim'], 
                                      edge_label=edge_label)
    for itr in range(0, 10): # @todo: the convergence condition?
        G_new = G.copy()
        # update vertex labels.
        # pre-compute h_i0 for each label.
#        for label in get_node_labels(Gn, node_label):
#            print(label)
#        for nd in G.nodes(data=True):
#            pass
        if not ds_attrs['node_attr_dim']: # labels are symbolic
            for nd, _ in G.nodes(data=True):
                h_i0_list = []
                label_list = []
                for label in get_node_labels(Gn, node_label):
                    h_i0 = 0
                    for idx, g in enumerate(Gn):
                        pi_i = pi_p[idx][nd]
                        if g.has_node(pi_i) and g.nodes[pi_i][node_label] == label:
                            h_i0 += 1
                    h_i0_list.append(h_i0)
                    label_list.append(label)
                # choose one of the best randomly.
                idx_max = np.argwhere(h_i0_list == np.max(h_i0_list)).flatten().tolist()
                idx_rdm = random.randint(0, len(idx_max) - 1)
                G_new.nodes[nd][node_label] = label_list[idx_max[idx_rdm]]
        else: # labels are non-symbolic
            for nd, _ in G.nodes(data=True):
                Si_norm = 0
                phi_i_bar = np.array([0.0 for _ in range(ds_attrs['node_attr_dim'])])
                for idx, g in enumerate(Gn):
                    pi_i = pi_p[idx][nd]
                    if g.has_node(pi_i): #@todo: what if no g has node? phi_i_bar = 0?
                        Si_norm += 1
                        phi_i_bar += np.array([float(itm) for itm in g.nodes[pi_i]['attributes']])                
                phi_i_bar /= Si_norm
                G_new.nodes[nd]['attributes'] = phi_i_bar
                                            
        # update edge labels and adjacency matrix.
        if ds_attrs['edge_labeled']:
            for nd1, nd2, _ in G.edges(data=True):
                h_ij0_list = []
                label_list = []
                for label in get_edge_labels(Gn, edge_label):
                    h_ij0 = 0
                    for idx, g in enumerate(Gn):
                        pi_i = pi_p[idx][nd1]
                        pi_j = pi_p[idx][nd2]
                        h_ij0_p = (g.has_node(pi_i) and g.has_node(pi_j) and 
                                   g.has_edge(pi_i, pi_j) and 
                                   g.edges[pi_i, pi_j][edge_label] == label)
                        h_ij0 += h_ij0_p
                    h_ij0_list.append(h_ij0)
                    label_list.append(label)
                # choose one of the best randomly.
                idx_max = np.argwhere(h_ij0_list == np.max(h_ij0_list)).flatten().tolist()
                h_ij0_max = h_ij0_list[idx_max[0]]
                idx_rdm = random.randint(0, len(idx_max) - 1)
                best_label = label_list[idx_max[idx_rdm]]
                       
                # check whether a_ij is 0 or 1.
                sij_norm = 0
                for idx, g in enumerate(Gn):
                    pi_i = pi_p[idx][nd1]
                    pi_j = pi_p[idx][nd2]
                    if g.has_node(pi_i) and g.has_node(pi_j) and g.has_edge(pi_i, pi_j):
                       sij_norm += 1
                if h_ij0_max > len(Gn) * c_er / c_es + sij_norm * (1 - (c_er + c_ei) / c_es):
                    if not G_new.has_edge(nd1, nd2):
                        G_new.add_edge(nd1, nd2)
                    G_new.edges[nd1, nd2][edge_label] = best_label
                else:
                    if G_new.has_edge(nd1, nd2):
                        G_new.remove_edge(nd1, nd2)                
        else: # if edges are unlabeled
            for nd1, nd2, _ in G.edges(data=True):
                sij_norm = 0
                for idx, g in enumerate(Gn):
                    pi_i = pi_p[idx][nd1]
                    pi_j = pi_p[idx][nd2]
                    if g.has_node(pi_i) and g.has_node(pi_j) and g.has_edge(pi_i, pi_j):
                       sij_norm += 1
                if sij_norm > len(Gn) * c_er / (c_er + c_ei):
                    if not G_new.has_edge(nd1, nd2):
                        G_new.add_edge(nd1, nd2)
                else:
                    if G_new.has_edge(nd1, nd2):
                        G_new.remove_edge(nd1, nd2)
                        
        G = G_new.copy()
        
        # update pi_p
        pi_p = []
        for idx1, G_p in enumerate(Gn):
            dist_tmp, pi_tmp, _ = GED(G, G_p)
            pi_p.append(pi_tmp)
    
    return G


def GED(g1, g2, lib='gedlib'):
    """
    Compute GED.
    """
    if lib == 'gedlib':
        # transform dataset to the 'xml' file as the GedLib required.
        saveDataset([g1, g2], [None, None], group='xml', filename='ged_tmp/tmp')
#        script.appel()
        script.PyRestartEnv()
        script.PyLoadGXLGraph('ged_tmp/', 'ged_tmp/tmp.xml')
        listID = script.PyGetGraphIds()
        script.PySetEditCost("LETTER") #("CHEM_1")
        script.PyInitEnv()
        script.PySetMethod("IPFP", "")
        script.PyInitMethod()
        g = listID[0]
        h = listID[1]
        script.PyRunMethod(g, h)
        pi_forward, pi_backward = script.PyGetAllMap(g, h)
        upper = script.PyGetUpperBound(g, h)
        lower = script.PyGetLowerBound(g, h)        
        dis = upper
        
        # make the map label correct (label remove map as np.inf)
        nodes1 = [n for n in g1.nodes()]
        nodes2 = [n for n in g2.nodes()]
        nb1 = nx.number_of_nodes(g1)
        nb2 = nx.number_of_nodes(g2)
        pi_forward = [nodes2[pi] if pi < nb2 else np.inf for pi in pi_forward]
        pi_backward = [nodes1[pi] if pi < nb1 else np.inf for pi in pi_backward]                
        
    return dis, pi_forward, pi_backward


# --------------------------- These are tests --------------------------------#
    
def test_iam_with_more_graphs_as_init(Gn, G_candidate, c_ei=3, c_er=3, c_es=1, 
                                      node_label='atom', edge_label='bond_type'):
    """See my name, then you know what I do.
    """
    from tqdm import tqdm
#    Gn = Gn[0:10]
    Gn = [nx.convert_node_labels_to_integers(g) for g in Gn]
    
    # phase 1: initilize.
    # compute set-median.
    dis_min = np.inf
#    pi_p = []
    pi_all_forward = []
    pi_all_backward = []
    for idx1, G_p in tqdm(enumerate(G_candidate), desc='computing GEDs', file=sys.stdout):
        dist_sum = 0
        pi_all_forward.append([])
        pi_all_backward.append([])
        for idx2, G_p_prime in enumerate(Gn):
            dist_tmp, pi_tmp_forward, pi_tmp_backward = GED(G_p, G_p_prime)
            pi_all_forward[idx1].append(pi_tmp_forward)
            pi_all_backward[idx1].append(pi_tmp_backward)
            dist_sum += dist_tmp
        if dist_sum <= dis_min:
            dis_min = dist_sum
            G = G_p.copy()
            idx_min = idx1
    # list of edit operations.        
    pi_p_forward = pi_all_forward[idx_min]
    pi_p_backward = pi_all_backward[idx_min]
            
    # phase 2: iteration.
    ds_attrs = get_dataset_attributes(Gn + [G], attr_names=['edge_labeled', 'node_attr_dim'], 
                                      edge_label=edge_label)
    label_set = get_node_labels(Gn + [G], node_label)
    for itr in range(0, 10): # @todo: the convergence condition?
        G_new = G.copy()
        # update vertex labels.
        # pre-compute h_i0 for each label.
#        for label in get_node_labels(Gn, node_label):
#            print(label)
#        for nd in G.nodes(data=True):
#            pass
        if not ds_attrs['node_attr_dim']: # labels are symbolic
            for nd in G.nodes():
                h_i0_list = []
                label_list = []
                for label in label_set:
                    h_i0 = 0
                    for idx, g in enumerate(Gn):
                        pi_i = pi_p_forward[idx][nd]
                        if g.has_node(pi_i) and g.nodes[pi_i][node_label] == label:
                            h_i0 += 1
                    h_i0_list.append(h_i0)
                    label_list.append(label)
                # choose one of the best randomly.
                idx_max = np.argwhere(h_i0_list == np.max(h_i0_list)).flatten().tolist()
                idx_rdm = random.randint(0, len(idx_max) - 1)
                G_new.nodes[nd][node_label] = label_list[idx_max[idx_rdm]]
        else: # labels are non-symbolic
            for nd in G.nodes():
                Si_norm = 0
                phi_i_bar = np.array([0.0 for _ in range(ds_attrs['node_attr_dim'])])
                for idx, g in enumerate(Gn):
                    pi_i = pi_p_forward[idx][nd]
                    if g.has_node(pi_i): #@todo: what if no g has node? phi_i_bar = 0?
                        Si_norm += 1
                        phi_i_bar += np.array([float(itm) for itm in g.nodes[pi_i]['attributes']])                
                phi_i_bar /= Si_norm
                G_new.nodes[nd]['attributes'] = phi_i_bar
                                            
        # update edge labels and adjacency matrix.
        if ds_attrs['edge_labeled']:
            for nd1, nd2, _ in G.edges(data=True):
                h_ij0_list = []
                label_list = []
                for label in get_edge_labels(Gn, edge_label):
                    h_ij0 = 0
                    for idx, g in enumerate(Gn):
                        pi_i = pi_p_forward[idx][nd1]
                        pi_j = pi_p_forward[idx][nd2]
                        h_ij0_p = (g.has_node(pi_i) and g.has_node(pi_j) and 
                                   g.has_edge(pi_i, pi_j) and 
                                   g.edges[pi_i, pi_j][edge_label] == label)
                        h_ij0 += h_ij0_p
                    h_ij0_list.append(h_ij0)
                    label_list.append(label)
                # choose one of the best randomly.
                idx_max = np.argwhere(h_ij0_list == np.max(h_ij0_list)).flatten().tolist()
                h_ij0_max = h_ij0_list[idx_max[0]]
                idx_rdm = random.randint(0, len(idx_max) - 1)
                best_label = label_list[idx_max[idx_rdm]]
                       
                # check whether a_ij is 0 or 1.
                sij_norm = 0
                for idx, g in enumerate(Gn):
                    pi_i = pi_p_forward[idx][nd1]
                    pi_j = pi_p_forward[idx][nd2]
                    if g.has_node(pi_i) and g.has_node(pi_j) and g.has_edge(pi_i, pi_j):
                       sij_norm += 1
                if h_ij0_max > len(Gn) * c_er / c_es + sij_norm * (1 - (c_er + c_ei) / c_es):
                    if not G_new.has_edge(nd1, nd2):
                        G_new.add_edge(nd1, nd2)
                    G_new.edges[nd1, nd2][edge_label] = best_label
                else:
                    if G_new.has_edge(nd1, nd2):
                        G_new.remove_edge(nd1, nd2)                
        else: # if edges are unlabeled
            # @todo: works only for undirected graphs.
            for nd1 in range(nx.number_of_nodes(G)):
                for nd2 in range(nd1 + 1, nx.number_of_nodes(G)):
                    sij_norm = 0
                    for idx, g in enumerate(Gn):
                        pi_i = pi_p_forward[idx][nd1]
                        pi_j = pi_p_forward[idx][nd2]
                        if g.has_node(pi_i) and g.has_node(pi_j) and g.has_edge(pi_i, pi_j):
                           sij_norm += 1
                    if sij_norm > len(Gn) * c_er / (c_er + c_ei):
                        if not G_new.has_edge(nd1, nd2):
                            G_new.add_edge(nd1, nd2)
                    elif sij_norm < len(Gn) * c_er / (c_er + c_ei):
                        if G_new.has_edge(nd1, nd2):
                            G_new.remove_edge(nd1, nd2)
                    # do not change anything when equal.
                        
        G = G_new.copy()
        
        # update pi_p
        pi_p_forward = []
        for G_p in Gn:
            dist_tmp, pi_tmp_forward, pi_tmp_backward = GED(G, G_p)
            pi_p_forward.append(pi_tmp_forward)
    
    return G


def test_iam_moreGraphsAsInit_tryAllPossibleBestGraphs_deleteNodesInIterations(
        Gn_median, Gn_candidate, c_ei=3, c_er=3, c_es=1, node_label='atom', 
        edge_label='bond_type', connected=True):
    """See my name, then you know what I do.
    """
    from tqdm import tqdm
#    Gn_median = Gn_median[0:10]
#    Gn_median = [nx.convert_node_labels_to_integers(g) for g in Gn_median]
    node_ir = np.inf # corresponding to the node remove and insertion.
    label_r = 'thanksdanny' # the label for node remove. # @todo: make this label unrepeatable.
    ds_attrs = get_dataset_attributes(Gn_median + Gn_candidate, 
                                      attr_names=['edge_labeled', 'node_attr_dim'], 
                                      edge_label=edge_label)

    
    def generate_graph(G, pi_p_forward, label_set):
        G_new_list = [G.copy()] # all "best" graphs generated in this iteration.
#        nx.draw_networkx(G)
#        import matplotlib.pyplot as plt
#        plt.show()
#        print(pi_p_forward)
                    
        # update vertex labels.
        # pre-compute h_i0 for each label.
#        for label in get_node_labels(Gn, node_label):
#            print(label)
#        for nd in G.nodes(data=True):
#            pass
        if not ds_attrs['node_attr_dim']: # labels are symbolic
            for ndi, (nd, _) in enumerate(G.nodes(data=True)):
                h_i0_list = []
                label_list = []
                for label in label_set:
                    h_i0 = 0
                    for idx, g in enumerate(Gn_median):
                        pi_i = pi_p_forward[idx][ndi]
                        if pi_i != node_ir and g.nodes[pi_i][node_label] == label:
                            h_i0 += 1
                    h_i0_list.append(h_i0)
                    label_list.append(label)
                # case when the node is to be removed.
                h_i0_remove = 0
                for idx, g in enumerate(Gn_median):
                    pi_i = pi_p_forward[idx][ndi]
                    if pi_i == node_ir:
                        h_i0_remove += 1
                h_i0_list.append(h_i0_remove)
                label_list.append(label_r)
                # get the best labels.
                idx_max = np.argwhere(h_i0_list == np.max(h_i0_list)).flatten().tolist()
                nlabel_best = [label_list[idx] for idx in idx_max]
                # generate "best" graphs with regard to "best" node labels.
                G_new_list_nd = []
                for g in G_new_list: # @todo: seems it can be simplified. The G_new_list will only contain 1 graph for now.
                    for nl in nlabel_best:
                        g_tmp = g.copy()
                        if nl == label_r:
                            g_tmp.remove_node(nd)
                        else:
                            g_tmp.nodes[nd][node_label] = nl
                        G_new_list_nd.append(g_tmp)
#                            nx.draw_networkx(g_tmp)
#                            import matplotlib.pyplot as plt
#                            plt.show()
#                            print(g_tmp.nodes(data=True))
#                            print(g_tmp.edges(data=True))
                G_new_list = G_new_list_nd[:]

        else: # labels are non-symbolic
            for ndi, (nd, _) in enumerate(G.nodes(data=True)):
                Si_norm = 0
                phi_i_bar = np.array([0.0 for _ in range(ds_attrs['node_attr_dim'])])
                for idx, g in enumerate(Gn_median):
                    pi_i = pi_p_forward[idx][ndi]
                    if g.has_node(pi_i): #@todo: what if no g has node? phi_i_bar = 0?
                        Si_norm += 1
                        phi_i_bar += np.array([float(itm) for itm in g.nodes[pi_i]['attributes']])                
                phi_i_bar /= Si_norm
                G_new_list[0].nodes[nd]['attributes'] = phi_i_bar
                                            
        # update edge labels and adjacency matrix.
        if ds_attrs['edge_labeled']:
            for nd1, nd2, _ in G.edges(data=True):
                h_ij0_list = []
                label_list = []
                for label in get_edge_labels(Gn_median, edge_label):
                    h_ij0 = 0
                    for idx, g in enumerate(Gn_median):
                        pi_i = pi_p_forward[idx][nd1]
                        pi_j = pi_p_forward[idx][nd2]
                        h_ij0_p = (g.has_node(pi_i) and g.has_node(pi_j) and 
                                   g.has_edge(pi_i, pi_j) and 
                                   g.edges[pi_i, pi_j][edge_label] == label)
                        h_ij0 += h_ij0_p
                    h_ij0_list.append(h_ij0)
                    label_list.append(label)
                # choose one of the best randomly.
                idx_max = np.argwhere(h_ij0_list == np.max(h_ij0_list)).flatten().tolist()
                h_ij0_max = h_ij0_list[idx_max[0]]
                idx_rdm = random.randint(0, len(idx_max) - 1)
                best_label = label_list[idx_max[idx_rdm]]
                       
                # check whether a_ij is 0 or 1.
                sij_norm = 0
                for idx, g in enumerate(Gn_median):
                    pi_i = pi_p_forward[idx][nd1]
                    pi_j = pi_p_forward[idx][nd2]
                    if g.has_node(pi_i) and g.has_node(pi_j) and g.has_edge(pi_i, pi_j):
                       sij_norm += 1
                if h_ij0_max > len(Gn_median) * c_er / c_es + sij_norm * (1 - (c_er + c_ei) / c_es):
                    if not G_new.has_edge(nd1, nd2):
                        G_new.add_edge(nd1, nd2)
                    G_new.edges[nd1, nd2][edge_label] = best_label
                else:
                    if G_new.has_edge(nd1, nd2):
                        G_new.remove_edge(nd1, nd2)                
        else: # if edges are unlabeled
            # @todo: works only for undirected graphs.
            nd_list = [n for n in G.nodes()]
            for g_tmp in G_new_list:
                for nd1i in range(nx.number_of_nodes(G)):
                    nd1 = nd_list[nd1i]
                    for nd2i in range(nd1i + 1, nx.number_of_nodes(G)):
                        nd2 = nd_list[nd2i]
                        sij_norm = 0
                        for idx, g in enumerate(Gn_median):
                            pi_i = pi_p_forward[idx][nd1i]
                            pi_j = pi_p_forward[idx][nd2i]
                            if g.has_node(pi_i) and g.has_node(pi_j) and g.has_edge(pi_i, pi_j):
                               sij_norm += 1
                        if sij_norm > len(Gn_median) * c_er / (c_er + c_ei):
                            # @todo: should we consider if nd1 and nd2 in g_tmp?
                            # or just add the edge anyway?
                            if g_tmp.has_node(nd1) and g_tmp.has_node(nd2) \
                                and not g_tmp.has_edge(nd1, nd2):
                                g_tmp.add_edge(nd1, nd2)
                        elif sij_norm < len(Gn_median) * c_er / (c_er + c_ei):
                            if g_tmp.has_edge(nd1, nd2):
                                g_tmp.remove_edge(nd1, nd2)
                        # do not change anything when equal.                        
        
        # find the best graph generated in this iteration and update pi_p.
        # @todo: should we update all graphs generated or just the best ones?
        dis_list, pi_forward_list = median_distance(G_new_list, Gn_median)
        # @todo: should we remove the identical and connectivity check? 
        # Don't know which is faster.
        G_new_list, idx_list = remove_duplicates(G_new_list)
        pi_forward_list = [pi_forward_list[idx] for idx in idx_list]
#        if connected == True:
#            G_new_list, idx_list = remove_disconnected(G_new_list)
#            pi_forward_list = [pi_forward_list[idx] for idx in idx_list]
#        idx_min_list = np.argwhere(dis_list == np.min(dis_list)).flatten().tolist()
#        dis_min = dis_list[idx_min_tmp_list[0]]
#        pi_forward_list = [pi_forward_list[idx] for idx in idx_min_list]
#        G_new_list = [G_new_list[idx] for idx in idx_min_list] 
        
#        for g in G_new_list:
#            import matplotlib.pyplot as plt 
#            nx.draw_networkx(g)
#            plt.show()
#            print(g.nodes(data=True))
#            print(g.edges(data=True))
        
        return G_new_list, pi_forward_list
    
    
    def median_distance(Gn, Gn_median, measure='ged', verbose=False):
        dis_list = []
        pi_forward_list = []
        for idx, G in tqdm(enumerate(Gn), desc='computing median distances', 
                           file=sys.stdout) if verbose else enumerate(Gn):
            dis_sum = 0
            pi_forward_list.append([])
            for G_p in Gn_median:
                dis_tmp, pi_tmp_forward, pi_tmp_backward = GED(G, G_p)
                pi_forward_list[idx].append(pi_tmp_forward)
                dis_sum += dis_tmp
            dis_list.append(dis_sum)
        return dis_list, pi_forward_list
    
    
    def best_median_graphs(Gn_candidate, dis_all, pi_all_forward):
        idx_min_list = np.argwhere(dis_all == np.min(dis_all)).flatten().tolist()
        dis_min = dis_all[idx_min_list[0]]
        pi_forward_min_list = [pi_all_forward[idx] for idx in idx_min_list]
        G_min_list = [Gn_candidate[idx] for idx in idx_min_list]
        return G_min_list, pi_forward_min_list, dis_min
    
    
    def iteration_proc(G, pi_p_forward):
        G_list = [G]
        pi_forward_list = [pi_p_forward]
        # iterations.
        for itr in range(0, 5): # @todo: the convergence condition?
#            print('itr is', itr)
            G_new_list = []
            pi_forward_new_list = []
            for idx, G in enumerate(G_list):
                label_set = get_node_labels(Gn_median + [G], node_label)                        
                G_tmp_list, pi_forward_tmp_list = generate_graph(
                    G, pi_forward_list[idx], label_set)
                G_new_list += G_tmp_list
                pi_forward_new_list += pi_forward_tmp_list
            G_list = G_new_list[:]
            pi_forward_list = pi_forward_new_list[:]
        
        G_list, idx_list = remove_duplicates(G_list)
        pi_forward_list = [pi_forward_list[idx] for idx in idx_list]
            
#        import matplotlib.pyplot as plt
#        for g in G_list:             
#            nx.draw_networkx(g)
#            plt.show()
#            print(g.nodes(data=True))
#            print(g.edges(data=True))
            
        return G_list, pi_forward_list # do we return all graphs or the best ones?
    
    
    def remove_duplicates(Gn):
        """Remove duplicate graphs from list.
        """
        Gn_new = []
        idx_list = []
        for idx, g in enumerate(Gn):
            dupl = False
            for g_new in Gn_new:
                if graph_isIdentical(g_new, g):
                    dupl = True
                    break
            if not dupl:
                Gn_new.append(g)
                idx_list.append(idx)
        return Gn_new, idx_list
    
    
    def remove_disconnected(Gn):
        """Remove disconnected graphs from list.
        """
        Gn_new = []
        idx_list = []
        for idx, g in enumerate(Gn):
            if nx.is_connected(g):
                Gn_new.append(g)
                idx_list.append(idx)
        return Gn_new, idx_list

   
    # phase 1: initilize.
    # compute set-median.
    dis_min = np.inf
    dis_all, pi_all_forward = median_distance(Gn_candidate, Gn_median)
    # find all smallest distances.
    idx_min_list = np.argwhere(dis_all == np.min(dis_all)).flatten().tolist()
    dis_min = dis_all[idx_min_list[0]]
    
    # phase 2: iteration.
    G_list = []
    for idx_min in idx_min_list[::-1]:
#        print('idx_min is', idx_min)
        G = Gn_candidate[idx_min].copy()
        # list of edit operations.        
        pi_p_forward = pi_all_forward[idx_min]
#        pi_p_backward = pi_all_backward[idx_min]        
        Gi_list, pi_i_forward_list = iteration_proc(G, pi_p_forward)            
        G_list += Gi_list
        
    G_list, _ = remove_duplicates(G_list)
    if connected == True:
        G_list_con, _ = remove_disconnected(G_list)
    # if there is no connected graphs at all, then remain the disconnected ones.
    if len(G_list_con) > 0: # @todo: ??????????????????????????
        G_list = G_list_con

#    import matplotlib.pyplot as plt 
#    for g in G_list:
#        nx.draw_networkx(g)
#        plt.show()
#        print(g.nodes(data=True))
#        print(g.edges(data=True))
    
    # get the best median graphs
    dis_all, pi_all_forward = median_distance(G_list, Gn_median)
    G_min_list, pi_forward_min_list, dis_min = best_median_graphs(
            G_list, dis_all, pi_all_forward)
#    for g in G_min_list:
#        nx.draw_networkx(g)
#        plt.show()
#        print(g.nodes(data=True))
#        print(g.edges(data=True))
    return G_min_list


if __name__ == '__main__':
    from pygraph.utils.graphfiles import loadDataset
    ds = {'name': 'MUTAG', 'dataset': '../datasets/MUTAG/MUTAG.mat',
          'extra_params': {'am_sp_al_nl_el': [0, 0, 3, 1, 2]}}  # node/edge symb
#    ds = {'name': 'Letter-high', 'dataset': '../datasets/Letter-high/Letter-high_A.txt',
#          'extra_params': {}} # node nsymb
#    ds = {'name': 'Acyclic', 'dataset': '../datasets/monoterpenoides/trainset_9.ds',
#          'extra_params': {}}
    Gn, y_all = loadDataset(ds['dataset'], extra_params=ds['extra_params'])

    iam(Gn)