Project: s41467-024-45598-0 | Function: gen_topol_feats (python)

system: You are an expert Python programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
Follow Python best practices and maintain consistent code style.
Return **only** the complete Python function code.

user: Complete this Python function:

**DESCRIPTION:** Generates topological features for network link prediction including degree metrics, clustering coefficients, centrality measures, and SVD-based features

**KEY TERMS:** {
  "A_orig": "original adjacency matrix",
  "A": "training or holdout adjacency matrix",
  "edge_s": "sample set of edges",
  "ave_deg_net": "average degree",
  "var_deg_net": "variance of degree distribution",
  "ave_clust_net": "average clustering coefficient",
  "page_rank": "PageRank values",
  "ktz_cent": "Katz centrality",
  "jacc_coeff": "Jaccard coefficient",
  "adam_adar": "Adamic-Adar index"
}

**CONTEXT CODE:**     edges: edge list of the given network

    Examples:
    -------
    >>> nodes, edges = adj_to_nodes_edges(A)
    """
    
    nodes, edge_tr = adj_to_nodes_edges(A_tr)
    nsim_id = 0
    np.random.seed(nsim_id)

    A_diff = A_ho - A_tr
    e_diff = sparse.find(sparse.triu(A_diff,1)) # true candidates
    A_ho_aux = -1*A_ho + 1
    ne_ho = sparse.find(sparse.triu(A_ho_aux,1)) # false candidates
    Nsamples = 2000 # number of samples
    edge_t = [] # list of true edges (positive samples)
    edge_f = [] # list of false edges (negative samples)
    for ll in range(Nsamples):
	    edge_t_idx_aux = np.random.randint(len(e_diff[0]))
	    edge_f_idx_aux = np.random.randint(len(ne_ho[0]))
	    edge_t.append((e_diff[0][edge_t_idx_aux],e_diff[1][edge_t_idx_aux]))
	    edge_f.append((ne_ho[0][edge_f_idx_aux],ne_ho[1][edge_f_idx_aux]))
	
	# store for later use
    if not os.path.isdir("./edge_tf_tr/"):
	    os.mkdir("./edge_tf_tr/")
    np.savetxt("./edge_tf_tr/edge_t.txt",edge_t,fmt='%u')
    np.savetxt("./edge_tf_tr/edge_f.txt",edge_f,fmt='%u')
    
    A_diff = A_orig - A_ho
    e_diff = sparse.find(sparse.triu(A_diff,1)) # true candidates
    A_orig_aux = -1*A_orig + 1
    ne_orig = sparse.find(sparse.triu(A_orig_aux,1)) # false candidates
    Nsamples = 10000 # number of samples
    edge_tt = [] # list of true edges (positive samples)
    edge_ff = [] # list of false edges (negative samples)
    for ll in range(Nsamples):
        edge_tt_idx_aux = np.random.randint(len(e_diff[0]))
        edge_ff_idx_aux = np.random.randint(len(ne_orig[0]))
        edge_tt.append((e_diff[0][edge_tt_idx_aux],e_diff[1][edge_tt_idx_aux]))
        edge_ff.append((ne_orig[0][edge_ff_idx_aux],ne_orig[1][edge_ff_idx_aux]))
    
    # store for later use
    if not os.path.isdir("./edge_tf_ho/"):
        os.mkdir("./edge_tf_ho/")
    np.savetxt("./edge_tf_ho/edge_t.txt",edge_tt,fmt='%u')
    np.savetxt("./edge_tf_ho/edge_f.txt",edge_ff,fmt='%u')
    return edge_t, edge_f, edge_tt, edge_ff

def gen_topol_feats(A_orig, A, edge_s): 
    
    """ 
    This function generates the topological features for matrix A (A_tr or A_ho) over edge samples edge_s (edge_tr or edge_ho).

    Input and Parameters:
    -------
    A: the training or holdout adjacency matrix that the topological features are going to be computed over
    A_orig: the original adjacency matrix
    edge_s: the sample set of training or holdout edges that the topological features are going to be computed over

    Returns:
    -------
    df_feat: data frame of features

    Examples:
    -------
    >>> gen_topol_feats(A_orig, A_tr, edge_tr)
    >>> gen_topol_feats(A_orig, A_ho, edge_ho)
    """
    
    # MASKED: Generates topological features for network link prediction including degree metrics, clustering coefficients, centrality measures, and SVD-based features implementation
    raise NotImplementedError("This function is masked for testing purposes.")




def creat_full_set(df_t,df_f):
    
    """ 
    This reads dataframes created for positive and negative class, join them with their associated label.

    Input and Parameters:
    -------
    df_t: datafram of features for true edges
    df_f: datafram of features for true non-edges

    Returns
    -------
    df_all: a data frames with columns of features and ground truth 

    Examples:
    -------
    df_all = creat_full_set(df_t,df_f)
    """
    df_t = df_t.drop_duplicates(subset=['i','j'], keep="first")
    df_f = df_f.drop_duplicates(subset=['i','j'], keep="first")

    df_t.insert(2, "TP", 1, True)
    df_f.insert(2, "TP", 0, True)
    
    df_all = [df_t, df_f]
    df_all = pd.concat(df_all)
    
    # data cleaning
    df_all.loc[df_all['short_path'] == np.inf,'short_path'] = 1000*max(df_all.loc[~(df_all['short_path'] == np.inf),'short_path'])
    df_all.loc[df_all['diam_net'] == np.inf,'diam_net'] = 1e6
     
    return df_all


def creat_numpy_files(dir_results, df_ho, df_tr):
    
    """ 
    This function reads dataframes created for positive and negative classes, join them with their associated label.

    Input and Parameters:
    -------
    df_tr: datafram of features/ground truth for positive and negative class for model selection
    df_ho: datafram of features/ground truth for positive and negative class for held out model performance

    Returns:
    -------
    save numpy files of X_train_i and y_train_i for 5 folds, also X_Eseen/X_Eunseen, y_Eseen/y_Eunseen in dir_results

    Example:
    -------
    creat_numpy_files(dir_results, df_ho, df_tr)
    """
    
    feature_set = ['com_ne', 'ave_deg_net', 'var_deg_net', 'ave_clust_net',
           'num_triangles_1', 'num_triangles_2', 'page_rank_pers_edges',
           'pag_rank1', 'pag_rank2', 'clust_coeff1', 'clust_coeff2',
           'ave_neigh_deg1', 'ave_neigh_deg2', 'eig_cent1', 'eig_cent2',
           'deg_cent1', 'deg_cent2', 'clos_cent1', 'clos_cent2', 'betw_cent1',
           'betw_cent2', 'load_cent1', 'load_cent2', 'ktz_cent1', 'ktz_cent2',
           'pref_attach', 'LHN', 'svd_edges', 'svd_edges_dot', 'svd_edges_mean',
           'svd_edges_approx', 'svd_edges_dot_approx', 'svd_edges_mean_approx',
           'short_path', 'deg_assort', 'transit_net', 'diam_net',
           'jacc_coeff', 'res_alloc_ind', 'adam_adar' , 'num_nodes','num_edges']  

    X_test_heldout = df_ho
    y_test_heldout = np.array(df_ho.TP)
    
    
    X_train_orig = df_tr
    y_train_orig = np.array(df_tr.TP)

    skf = StratifiedKFold(n_splits=5,shuffle=True)
    skf.get_n_splits(X_train_orig, y_train_orig)


Complete the function implementation replacing "raise NotImplementedError".