Esempio n. 1
0
def test_get_metrics(metric):
    """
    Test various wrappers for getting nx graph metrics
    """
    base_dir = str(Path(__file__).parent / "examples")
    est_path = f"{base_dir}/miscellaneous/sub-0021001_rsn-Default_nodetype-parc_model-sps_template-MNI152_T1_thrtype-DENS_thr-0.19.npy"

    in_mat = np.load(est_path)
    G = nx.from_numpy_array(in_mat)
    ci = np.ones(in_mat.shape[0])
    metric_list_names = []
    net_met_val_list_final = []

    if metric == 'participation':
        metric_list_names, net_met_val_list_final = \
            netstats.get_participation(in_mat, ci, metric_list_names, net_met_val_list_final)
        assert len(metric_list_names) == len(
            netstats.participation_coef(in_mat, ci)) + 1
        assert len(net_met_val_list_final) == len(
            netstats.participation_coef(in_mat, ci)) + 1
    elif metric == 'diversity':
        metric_list_names, net_met_val_list_final = \
            netstats.get_diversity(in_mat, ci, metric_list_names, net_met_val_list_final)
        assert len(metric_list_names) == np.shape(
            netstats.diversity_coef_sign(in_mat, ci))[1] + 1
        assert len(net_met_val_list_final) == np.shape(
            netstats.diversity_coef_sign(in_mat, ci))[1] + 1
    elif metric == 'local_efficiency':
        metric_list_names, net_met_val_list_final = \
            netstats.get_local_efficiency(G, metric_list_names, net_met_val_list_final)
        assert len(metric_list_names) == len(netstats.local_efficiency(G)) + 1
        assert len(net_met_val_list_final) == len(
            netstats.local_efficiency(G)) + 1
    elif metric == 'comm_centrality':
        metric_list_names, net_met_val_list_final = \
            netstats.get_comm_centrality(G, metric_list_names, net_met_val_list_final)
        assert len(metric_list_names) == len(
            nx.algorithms.communicability_betweenness_centrality(G)) + 1
        assert len(net_met_val_list_final) == len(
            nx.algorithms.communicability_betweenness_centrality(G)) + 1
    elif metric == 'rich_club_coeff':
        metric_list_names, net_met_val_list_final = \
            netstats.get_rich_club_coeff(G, metric_list_names, net_met_val_list_final)
        assert len(metric_list_names) == len(
            nx.algorithms.rich_club_coefficient(G)) + 1
        assert len(net_met_val_list_final) == len(
            nx.algorithms.rich_club_coefficient(G)) + 1
Esempio n. 2
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def test_participation_coef():
    base_dir = str(Path(__file__).parent/"examples")
    in_mat = np.load(base_dir + '/002/fmri/002_Default_est_cov_0.95prop_TESTmm_3nb_2fwhm_0.1Hz.npy')
    ci = np.ones(in_mat.shape[0])
    ci_dim = int(np.shape(ci)[0])
    W = np.random.rand(ci_dim, ci_dim)

    start_time = time.time()
    P = netstats.participation_coef(W, ci, degree='undirected')
    print("%s%s%s" % ('thresh_and_fit (Functional, proportional thresholding) --> finished: ',
                      str(np.round(time.time() - start_time, 1)), 's'))
    assert P is not None
Esempio n. 3
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def test_participation_coef():
    """
    Test for participation_coef functionality
    """
    base_dir = str(Path(__file__).parent/"examples")
    in_mat = np.load(f"{base_dir}/miscellaneous/graphs/002_modality-func_rsn-Default_model-cov_nodetype-spheres-2mm_smooth-2fwhm_hpass-0.1Hz_thrtype-PROP_thr-0.95.npy")
    ci = np.ones(in_mat.shape[0])
    ci_dim = int(np.shape(ci)[0])
    W = np.random.rand(ci_dim, ci_dim)

    start_time = time.time()
    P = netstats.participation_coef(W, ci, degree='undirected')
    print("%s%s%s" % ('thresh_and_fit (Functional, proportional thresholding) --> finished: ',
                      str(np.round(time.time() - start_time, 1)), 's'))
    assert P is not None
Esempio n. 4
0
def extractnetstats(ID,
                    network,
                    thr,
                    conn_model,
                    est_path,
                    roi,
                    prune,
                    node_size,
                    norm,
                    binary,
                    custom_weight=None):
    """
    Function interface for performing fully-automated graph analysis.

    Parameters
    ----------
    ID : str
        A subject id or other unique identifier.
    network : str
        Resting-state network based on Yeo-7 and Yeo-17 naming (e.g. 'Default') used to filter nodes in the study of
        brain subgraphs.
    thr : float
        The value, between 0 and 1, used to threshold the graph using any variety of methods
        triggered through other options.
    conn_model : str
       Connectivity estimation model (e.g. corr for correlation, cov for covariance, sps for precision covariance,
       partcorr for partial correlation). sps type is used by default.
    est_path : str
        File path to the thresholded graph, conn_matrix_thr, saved as a numpy array in .npy format.
    roi : str
        File path to binarized/boolean region-of-interest Nifti1Image file.
    prune : bool
        Indicates whether to prune final graph of disconnected nodes/isolates.
    node_size : int
        Spherical centroid node size in the case that coordinate-based centroids
        are used as ROI's.
    norm : int
        Indicates method of normalizing resulting graph.
    binary : bool
        Indicates whether to binarize resulting graph edges to form an
        unweighted graph.
    custom_weight : float
        The edge attribute that holds the numerical value used as a weight.
        If None, then each edge has weight 1. Default is None.

    Returns
    -------
    out_path : str
        Path to .csv file where graph analysis results are saved.
    """
    import pandas as pd
    import yaml
    try:
        import cPickle as pickle
    except ImportError:
        import _pickle as pickle
    from pathlib import Path
    from pynets import thresholding, utils

    # Advanced options
    fmt = 'edgelist_ssv'
    est_path_fmt = "%s%s" % ('.', est_path.split('.')[-1])

    # Load and threshold matrix
    if est_path_fmt == '.txt':
        in_mat_raw = np.array(np.genfromtxt(est_path))
    else:
        in_mat_raw = np.array(np.load(est_path))

    # De-diagnal
    in_mat = np.array(np.array(thresholding.autofix(in_mat_raw)))

    # Normalize connectivity matrix
    # Force edges to values between 0-1
    if norm == 1:
        in_mat = thresholding.normalize(in_mat)
    # Apply log10
    elif norm == 2:
        in_mat = np.log10(in_mat)
    else:
        pass

    # Correct nan's and inf's
    in_mat[np.isnan(in_mat)] = 0
    in_mat[np.isinf(in_mat)] = 1

    # Get hyperbolic tangent (i.e. fischer r-to-z transform) of matrix if non-covariance
    if (conn_model == 'corr') or (conn_model == 'partcorr'):
        in_mat = np.arctanh(in_mat)

    # Binarize graph
    if binary is True:
        in_mat = thresholding.binarize(in_mat)

    # Get dir_path
    dir_path = os.path.dirname(os.path.realpath(est_path))

    # Load numpy matrix as networkx graph
    G_pre = nx.from_numpy_matrix(in_mat)

    # Prune irrelevant nodes (i.e. nodes who are fully disconnected from the graph and/or those whose betweenness
    # centrality are > 3 standard deviations below the mean)
    if prune == 1:
        [G, _] = prune_disconnected(G_pre)
    elif prune == 2:
        [G, _] = most_important(G_pre)
    else:
        G = G_pre

    # Get corresponding matrix
    in_mat = np.array(nx.to_numpy_matrix(G))

    # Saved pruned
    if (prune != 0) and (prune is not None):
        final_mat_path = "%s%s%s" % (est_path.split(est_path_fmt)[0],
                                     '_pruned_mat', est_path_fmt)
        utils.save_mat(in_mat, final_mat_path, fmt)

    # Print graph summary
    print("%s%.2f%s" % ('\n\nThreshold: ', 100 * float(thr), '%'))
    print("%s%s" % ('Source File: ', est_path))
    info_list = list(nx.info(G).split('\n'))[2:]
    for i in info_list:
        print(i)

    if nx.is_connected(G) is True:
        frag = False
        print('Graph is connected...')
    else:
        frag = True
        print('Warning: Graph is fragmented...\n')

    # Create Length matrix
    mat_len = thresholding.weight_conversion(in_mat, 'lengths')

    # Load numpy matrix as networkx graph
    G_len = nx.from_numpy_matrix(mat_len)

    # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
    # # # # Calculate global and local metrics from graph G # # # #
    # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
    import community
    from networkx.algorithms import degree_assortativity_coefficient, average_clustering, average_shortest_path_length, degree_pearson_correlation_coefficient, graph_number_of_cliques, transitivity, betweenness_centrality, eigenvector_centrality, communicability_betweenness_centrality, clustering, degree_centrality, rich_club_coefficient, sigma
    from pynets.stats.netstats import average_local_efficiency, global_efficiency, participation_coef, participation_coef_sign, diversity_coef_sign
    # For non-nodal scalar metrics from custom functions, add the name of the function to metric_list and add the
    # function (with a G-only input) to the netstats module.
    metric_list_glob = [
        global_efficiency, average_local_efficiency,
        degree_assortativity_coefficient, average_clustering,
        average_shortest_path_length, degree_pearson_correlation_coefficient,
        graph_number_of_cliques, transitivity, sigma
    ]
    metric_list_comm = ['louvain_modularity']
    # with open("%s%s" % (str(Path(__file__).parent), '/global_graph_measures.yaml'), 'r') as stream:
    #     try:
    #         metric_dict_global = yaml.load(stream)
    #         metric_list_global = metric_dict_global['metric_list_global']
    #         print("%s%s%s" % ('\n\nCalculating global measures:\n', metric_list_global, '\n\n'))
    #     except FileNotFoundError:
    #         print('Failed to parse global_graph_measures.yaml')

    with open(
            "%s%s" %
        (str(Path(__file__).parent), '/nodal_graph_measures.yaml'),
            'r') as stream:
        try:
            metric_dict_nodal = yaml.load(stream)
            metric_list_nodal = metric_dict_nodal['metric_list_nodal']
            print("%s%s%s" % ('\n\nCalculating nodal measures:\n',
                              metric_list_nodal, '\n\n'))
        except FileNotFoundError:
            print('Failed to parse nodal_graph_measures.yaml')

    # Note the use of bare excepts in preceding blocks. Typically, this is considered bad practice in python. Here,
    # we are exploiting it intentionally to facilitate uninterrupted, automated graph analysis even when algorithms are
    # undefined. In those instances, solutions are assigned NaN's.

    # Iteratively run functions from above metric list that generate single scalar output
    num_mets = len(metric_list_glob)
    net_met_arr = np.zeros([num_mets, 2], dtype='object')
    j = 0
    for i in metric_list_glob:
        met_name = str(i).split('<function ')[1].split(' at')[0]
        net_met = met_name
        try:
            try:
                net_met_val = raw_mets(G, i, custom_weight)
            except:
                print("%s%s%s" %
                      ('WARNING: ', net_met, ' failed for graph G.'))
                net_met_val = np.nan
        except:
            print("%s%s%s" %
                  ('WARNING: ', str(i), ' is undefined for graph G'))
            net_met_val = np.nan
        net_met_arr[j, 0] = net_met
        net_met_arr[j, 1] = net_met_val
        print(net_met)
        print(str(net_met_val))
        print('\n')
        j = j + 1
    net_met_val_list = list(net_met_arr[:, 1])

    # Create a list of metric names for scalar metrics
    metric_list_names = []
    net_met_val_list_final = net_met_val_list
    for i in net_met_arr[:, 0]:
        metric_list_names.append(i)

    # Run miscellaneous functions that generate multiple outputs
    # Calculate modularity using the Louvain algorithm
    if 'louvain_modularity' in metric_list_comm:
        try:
            ci = community.best_partition(G)
            modularity = community.community_louvain.modularity(ci, G)
            metric_list_names.append('modularity')
            net_met_val_list_final.append(modularity)
        except:
            print('Louvain modularity calculation is undefined for graph G')
            pass

    # Participation Coefficient by louvain community
    if 'participation_coefficient' in metric_list_nodal:
        try:
            if ci is None:
                raise KeyError(
                    'Participation coefficient cannot be calculated for graph G in the absence of a '
                    'community affiliation vector')
            if len(in_mat[in_mat < 0.0]) > 0:
                pc_vector = participation_coef_sign(in_mat, ci)
            else:
                pc_vector = participation_coef(in_mat, ci)
            print(
                '\nExtracting Participation Coefficient vector for all network nodes...'
            )
            pc_vals = list(pc_vector)
            pc_edges = list(range(len(pc_vector)))
            num_edges = len(pc_edges)
            pc_arr = np.zeros([num_edges + 1, 2], dtype='object')
            j = 0
            for i in range(num_edges):
                pc_arr[j, 0] = "%s%s" % (str(pc_edges[j]), '_partic_coef')
                try:
                    pc_arr[j, 1] = pc_vals[j]
                except:
                    print("%s%s%s" %
                          ('Participation coefficient is undefined for node ',
                           str(j), ' of graph G'))
                    pc_arr[j, 1] = np.nan
                j = j + 1
            # Add mean
            pc_arr[num_edges, 0] = 'average_participation_coefficient'
            nonzero_arr_partic_coef = np.delete(pc_arr[:, 1], [0])
            pc_arr[num_edges, 1] = np.mean(nonzero_arr_partic_coef)
            print("%s%s" % ('Mean Participation Coefficient across edges: ',
                            str(pc_arr[num_edges, 1])))
            for i in pc_arr[:, 0]:
                metric_list_names.append(i)
            net_met_val_list_final = net_met_val_list_final + list(pc_arr[:,
                                                                          1])
        except:
            print('Participation coefficient cannot be calculated for graph G')
            pass

    # Diversity Coefficient by louvain community
    if 'diversity_coefficient' in metric_list_nodal:
        try:
            if ci is None:
                raise KeyError(
                    'Diversity coefficient cannot be calculated for graph G in the absence of a community '
                    'affiliation vector')
            [dc_vector, _] = diversity_coef_sign(in_mat, ci)
            print(
                '\nExtracting Diversity Coefficient vector for all network nodes...'
            )
            dc_vals = list(dc_vector)
            dc_edges = list(range(len(dc_vector)))
            num_edges = len(dc_edges)
            dc_arr = np.zeros([num_edges + 1, 2], dtype='object')
            j = 0
            for i in range(num_edges):
                dc_arr[j, 0] = "%s%s" % (str(dc_edges[j]), '_diversity_coef')
                try:
                    dc_arr[j, 1] = dc_vals[j]
                except:
                    print("%s%s%s" %
                          ('Diversity coefficient is undefined for node ',
                           str(j), ' of graph G'))
                    dc_arr[j, 1] = np.nan
                j = j + 1
            # Add mean
            dc_arr[num_edges, 0] = 'average_diversity_coefficient'
            nonzero_arr_diversity_coef = np.delete(dc_arr[:, 1], [0])
            dc_arr[num_edges, 1] = np.mean(nonzero_arr_diversity_coef)
            print("%s%s" % ('Mean Diversity Coefficient across edges: ',
                            str(dc_arr[num_edges, 1])))
            for i in dc_arr[:, 0]:
                metric_list_names.append(i)
            net_met_val_list_final = net_met_val_list_final + list(dc_arr[:,
                                                                          1])
        except:
            print('Diversity coefficient cannot be calculated for graph G')
            pass

    # Local Efficiency
    if 'local_efficiency' in metric_list_nodal:
        try:
            le_vector = local_efficiency(G)
            print(
                '\nExtracting Local Efficiency vector for all network nodes...'
            )
            le_vals = list(le_vector.values())
            le_nodes = list(le_vector.keys())
            num_nodes = len(le_nodes)
            le_arr = np.zeros([num_nodes + 1, 2], dtype='object')
            j = 0
            for i in range(num_nodes):
                le_arr[j, 0] = "%s%s" % (str(le_nodes[j]), '_local_efficiency')
                try:
                    le_arr[j, 1] = le_vals[j]
                except:
                    print(
                        "%s%s%s" % ('Local efficiency is undefined for node ',
                                    str(j), ' of graph G'))
                    le_arr[j, 1] = np.nan
                j = j + 1
            le_arr[num_nodes, 0] = 'average_local_efficiency_nodewise'
            nonzero_arr_le = np.delete(le_arr[:, 1], [0])
            le_arr[num_nodes, 1] = np.mean(nonzero_arr_le)
            print("%s%s" % ('Mean Local Efficiency across nodes: ',
                            str(le_arr[num_nodes, 1])))
            for i in le_arr[:, 0]:
                metric_list_names.append(i)
            net_met_val_list_final = net_met_val_list_final + list(le_arr[:,
                                                                          1])
        except:
            print('Local efficiency cannot be calculated for graph G')
            pass

    # Local Clustering
    if 'local_clustering' in metric_list_nodal:
        try:
            cl_vector = clustering(G)
            print(
                '\nExtracting Local Clustering vector for all network nodes...'
            )
            cl_vals = list(cl_vector.values())
            cl_nodes = list(cl_vector.keys())
            num_nodes = len(cl_nodes)
            cl_arr = np.zeros([num_nodes + 1, 2], dtype='object')
            j = 0
            for i in range(num_nodes):
                cl_arr[j, 0] = "%s%s" % (str(cl_nodes[j]), '_local_clustering')
                try:
                    cl_arr[j, 1] = cl_vals[j]
                except:
                    print(
                        "%s%s%s" % ('Local clustering is undefined for node ',
                                    str(j), ' of graph G'))
                    cl_arr[j, 1] = np.nan
                j = j + 1
            cl_arr[num_nodes, 0] = 'average_local_efficiency_nodewise'
            nonzero_arr_cl = np.delete(cl_arr[:, 1], [0])
            cl_arr[num_nodes, 1] = np.mean(nonzero_arr_cl)
            print("%s%s" % ('Mean Local Clustering across nodes: ',
                            str(cl_arr[num_nodes, 1])))
            for i in cl_arr[:, 0]:
                metric_list_names.append(i)
            net_met_val_list_final = net_met_val_list_final + list(cl_arr[:,
                                                                          1])
        except:
            print('Local clustering cannot be calculated for graph G')
            pass

    # Degree centrality
    if 'degree_centrality' in metric_list_nodal:
        try:
            dc_vector = degree_centrality(G)
            print(
                '\nExtracting Degree Centrality vector for all network nodes...'
            )
            dc_vals = list(dc_vector.values())
            dc_nodes = list(dc_vector.keys())
            num_nodes = len(dc_nodes)
            dc_arr = np.zeros([num_nodes + 1, 2], dtype='object')
            j = 0
            for i in range(num_nodes):
                dc_arr[j,
                       0] = "%s%s" % (str(dc_nodes[j]), '_degree_centrality')
                try:
                    dc_arr[j, 1] = dc_vals[j]
                except:
                    print(
                        "%s%s%s" % ('Degree centrality is undefined for node ',
                                    str(j), ' of graph G'))
                    dc_arr[j, 1] = np.nan
                j = j + 1
            dc_arr[num_nodes, 0] = 'average_degree_cent'
            nonzero_arr_dc = np.delete(dc_arr[:, 1], [0])
            dc_arr[num_nodes, 1] = np.mean(nonzero_arr_dc)
            print("%s%s" % ('Mean Degree Centrality across nodes: ',
                            str(dc_arr[num_nodes, 1])))
            for i in dc_arr[:, 0]:
                metric_list_names.append(i)
            net_met_val_list_final = net_met_val_list_final + list(dc_arr[:,
                                                                          1])
        except:
            print('Degree centrality cannot be calculated for graph G')
            pass

    # Betweenness Centrality
    if 'betweenness_centrality' in metric_list_nodal:
        try:
            bc_vector = betweenness_centrality(G_len, normalized=True)
            print(
                '\nExtracting Betweeness Centrality vector for all network nodes...'
            )
            bc_vals = list(bc_vector.values())
            bc_nodes = list(bc_vector.keys())
            num_nodes = len(bc_nodes)
            bc_arr = np.zeros([num_nodes + 1, 2], dtype='object')
            j = 0
            for i in range(num_nodes):
                bc_arr[j, 0] = "%s%s" % (str(
                    bc_nodes[j]), '_betweenness_centrality')
                try:
                    bc_arr[j, 1] = bc_vals[j]
                except:
                    print("%s%s%s" %
                          ('Betweeness centrality is undefined for node ',
                           str(j), ' of graph G'))
                    bc_arr[j, 1] = np.nan
                j = j + 1
            bc_arr[num_nodes, 0] = 'average_betweenness_centrality'
            nonzero_arr_betw_cent = np.delete(bc_arr[:, 1], [0])
            bc_arr[num_nodes, 1] = np.mean(nonzero_arr_betw_cent)
            print("%s%s" % ('Mean Betweenness Centrality across nodes: ',
                            str(bc_arr[num_nodes, 1])))
            for i in bc_arr[:, 0]:
                metric_list_names.append(i)
            net_met_val_list_final = net_met_val_list_final + list(bc_arr[:,
                                                                          1])
        except:
            print('Betweenness centrality cannot be calculated for graph G')
            pass

    # Eigenvector Centrality
    if 'eigenvector_centrality' in metric_list_nodal:
        try:
            ec_vector = eigenvector_centrality(G, max_iter=1000)
            print(
                '\nExtracting Eigenvector Centrality vector for all network nodes...'
            )
            ec_vals = list(ec_vector.values())
            ec_nodes = list(ec_vector.keys())
            num_nodes = len(ec_nodes)
            ec_arr = np.zeros([num_nodes + 1, 2], dtype='object')
            j = 0
            for i in range(num_nodes):
                ec_arr[j, 0] = "%s%s" % (str(
                    ec_nodes[j]), '_eigenvector_centrality')
                try:
                    ec_arr[j, 1] = ec_vals[j]
                except:
                    print("%s%s%s" %
                          ('Eigenvector centrality is undefined for node ',
                           str(j), ' of graph G'))
                    ec_arr[j, 1] = np.nan
                j = j + 1
            ec_arr[num_nodes, 0] = 'average_eigenvector_centrality'
            nonzero_arr_eig_cent = np.delete(ec_arr[:, 1], [0])
            ec_arr[num_nodes, 1] = np.mean(nonzero_arr_eig_cent)
            print("%s%s" % ('Mean Eigenvector Centrality across nodes: ',
                            str(ec_arr[num_nodes, 1])))
            for i in ec_arr[:, 0]:
                metric_list_names.append(i)
            net_met_val_list_final = net_met_val_list_final + list(ec_arr[:,
                                                                          1])
        except:
            print('Eigenvector centrality cannot be calculated for graph G')
            pass

    # Communicability Centrality
    if 'communicability_centrality' in metric_list_nodal:
        try:
            cc_vector = communicability_betweenness_centrality(G,
                                                               normalized=True)
            print(
                '\nExtracting Communicability Centrality vector for all network nodes...'
            )
            cc_vals = list(cc_vector.values())
            cc_nodes = list(cc_vector.keys())
            num_nodes = len(cc_nodes)
            cc_arr = np.zeros([num_nodes + 1, 2], dtype='object')
            j = 0
            for i in range(num_nodes):
                cc_arr[j, 0] = "%s%s" % (str(
                    cc_nodes[j]), '_communicability_centrality')
                try:
                    cc_arr[j, 1] = cc_vals[j]
                except:
                    print("%s%s%s" %
                          ('Communicability centrality is undefined for node ',
                           str(j), ' of graph G'))
                    cc_arr[j, 1] = np.nan
                j = j + 1
            cc_arr[num_nodes, 0] = 'average_communicability_centrality'
            nonzero_arr_comm_cent = np.delete(cc_arr[:, 1], [0])
            cc_arr[num_nodes, 1] = np.mean(nonzero_arr_comm_cent)
            print("%s%s" % ('Mean Communicability Centrality across nodes: ',
                            str(cc_arr[num_nodes, 1])))
            for i in cc_arr[:, 0]:
                metric_list_names.append(i)
            net_met_val_list_final = net_met_val_list_final + list(cc_arr[:,
                                                                          1])
        except:
            print(
                'Communicability centrality cannot be calculated for graph G')
            pass

    # Rich club coefficient
    if 'rich_club_coefficient' in metric_list_nodal:
        try:
            rc_vector = rich_club_coefficient(G, normalized=True)
            print(
                '\nExtracting Rich Club Coefficient vector for all network nodes...'
            )
            rc_vals = list(rc_vector.values())
            rc_edges = list(rc_vector.keys())
            num_edges = len(rc_edges)
            rc_arr = np.zeros([num_edges + 1, 2], dtype='object')
            j = 0
            for i in range(num_edges):
                rc_arr[j, 0] = "%s%s" % (str(rc_edges[j]), '_rich_club')
                try:
                    rc_arr[j, 1] = rc_vals[j]
                except:
                    print("%s%s%s" %
                          ('Rich club coefficient is undefined for node ',
                           str(j), ' of graph G'))
                    rc_arr[j, 1] = np.nan
                j = j + 1
            # Add mean
            rc_arr[num_edges, 0] = 'average_rich_club_coefficient'
            nonzero_arr_rich_club = np.delete(rc_arr[:, 1], [0])
            rc_arr[num_edges, 1] = np.mean(nonzero_arr_rich_club)
            print("%s%s" % ('Mean Rich Club Coefficient across edges: ',
                            str(rc_arr[num_edges, 1])))
            for i in rc_arr[:, 0]:
                metric_list_names.append(i)
            net_met_val_list_final = net_met_val_list_final + list(rc_arr[:,
                                                                          1])
        except:
            print('Rich club coefficient cannot be calculated for graph G')
            pass

    if roi:
        met_list_picke_path = "%s%s%s%s" % (
            os.path.dirname(os.path.abspath(est_path)), '/net_met_list', "%s" %
            ("%s%s%s" % ('_', network, '_') if network else "_"),
            os.path.basename(roi).split('.')[0])
    else:
        if network:
            met_list_picke_path = "%s%s%s" % (os.path.dirname(
                os.path.abspath(est_path)), '/net_met_list_', network)
        else:
            met_list_picke_path = "%s%s" % (os.path.dirname(
                os.path.abspath(est_path)), '/net_met_list')
    pickle.dump(metric_list_names, open(met_list_picke_path, 'wb'), protocol=2)

    # And save results to csv
    out_path = utils.create_csv_path(ID, network, conn_model, thr, roi,
                                     dir_path, node_size)
    np.savetxt(out_path, net_met_val_list_final, delimiter='\t')

    if frag is True:
        out_path_neat = "%s%s" % (out_path.split('.csv')[0], '_frag_neat.csv')
    else:
        out_path_neat = "%s%s" % (out_path.split('.csv')[0], '_neat.csv')
    df = pd.DataFrame.from_dict(dict(
        zip(metric_list_names, net_met_val_list_final)),
                                orient='index').transpose()
    df.to_csv(out_path_neat, index=False)

    return out_path