Python networkx.from_scipy_sparse_matrix() Examples

def text_to_graph(text):
    import networkx as nx
    from sklearn.feature_extraction.text import TfidfVectorizer
    from sklearn.neighbors import kneighbors_graph

    # use tfidf to transform texts into feature vectors
    vectorizer = TfidfVectorizer()
    vectors = vectorizer.fit_transform(text)

    # build the graph which is full-connected
    N = vectors.shape[0]
    mat = kneighbors_graph(vectors, N, metric='cosine', mode='distance', include_self=True)
    mat.data = 1 - mat.data  # to similarity

    g = nx.from_scipy_sparse_matrix(mat, create_using=nx.Graph())

    return g 

def textrank_text_summarizer(documents, num_sentences=2,
                             feature_type='frequency'):
    
    vec, dt_matrix = build_feature_matrix(norm_sentences, 
                                      feature_type='tfidf')
    similarity_matrix = (dt_matrix * dt_matrix.T)
        
    similarity_graph = networkx.from_scipy_sparse_matrix(similarity_matrix)
    scores = networkx.pagerank(similarity_graph)   
    
    ranked_sentences = sorted(((score, index) 
                                for index, score 
                                in scores.items()), 
                              reverse=True)

    top_sentence_indices = [ranked_sentences[index][1] 
                            for index in range(num_sentences)]
    top_sentence_indices.sort()
    
    for index in top_sentence_indices:
        print sentences[index] 

def textrank_tfidf(sentences, topk=6):
    """
        使用tf-idf作为相似度, networkx.pagerank获取中心句子作为摘要
    :param sentences: str, docs of text
    :param topk:int
    :return:list
    """
    # 切句子
    sentences = list(cut_sentence(sentences))
    # tf-idf相似度
    matrix_norm = tdidf_sim(sentences)
    # 构建相似度矩阵
    tfidf_sim = nx.from_scipy_sparse_matrix(matrix_norm * matrix_norm.T)
    # nx.pagerank
    sens_scores = nx.pagerank(tfidf_sim)
    # 得分排序
    sen_rank = sorted(sens_scores.items(), key=lambda x: x[1], reverse=True)
    # 保留topk个, 防止越界
    topk = min(len(sentences), topk)
    # 返回原句子和得分
    return [(sr[1], sentences[sr[0]]) for sr in sen_rank][0:topk] 

def textrank_tfidf(sentences, topk=6):
    """
        使用tf-idf作为相似度, networkx.pagerank获取中心句子作为摘要
    :param sentences: str, docs of text
    :param topk:int
    :return:list
    """
    # 切句子
    sentences = list(cut_sentence(sentences))
    # tf-idf相似度
    matrix_norm = tdidf_sim(sentences)
    # 构建相似度矩阵
    tfidf_sim = nx.from_scipy_sparse_matrix(matrix_norm * matrix_norm.T)
    # nx.pagerank
    sens_scores = nx.pagerank(tfidf_sim)
    # 得分排序
    sen_rank = sorted(sens_scores.items(), key=lambda x: x[1], reverse=True)
    # 保留topk个, 防止越界
    topk = min(len(sentences), topk)
    # 返回原句子和得分
    return [(sr[1], sentences[sr[0]]) for sr in sen_rank][0:topk] 

def init_setup():
    data = Dataset(root='/tmp/', name=args.dataset, setting='gcn')

    data.features = normalize_feature(data.features)
    adj, features, labels = data.adj, data.features, data.labels

    StaticGraph.graph = nx.from_scipy_sparse_matrix(adj)
    dict_of_lists = nx.to_dict_of_lists(StaticGraph.graph)

    idx_train, idx_val, idx_test = data.idx_train, data.idx_val, data.idx_test
    device = torch.device('cuda') if args.ctx == 'gpu' else 'cpu'

    # black box setting
    adj, features, labels = preprocess(adj, features, labels, preprocess_adj=False, sparse=True, device=device)
    victim_model = load_victim_model(data, device=device, file_path=args.saved_model)
    setattr(victim_model, 'norm_tool',  GraphNormTool(normalize=True, gm='gcn', device=device))
    output = victim_model.predict(features, adj)
    loss_test = F.nll_loss(output[idx_test], labels[idx_test])
    acc_test = accuracy(output[idx_test], labels[idx_test])
    print("Test set results:",
          "loss= {:.4f}".format(loss_test.item()),
          "accuracy= {:.4f}".format(acc_test.item()))

    return features, labels, idx_val, idx_test, victim_model, dict_of_lists, adj 

def calculate_comment_tree_hirsch(comment_tree):
    comment_tree_nx = nx.from_scipy_sparse_matrix(comment_tree, create_using=nx.Graph())

    if len(comment_tree_nx) == 0:
        comment_tree_hirsch = 0.0
    else:
        node_to_depth = nx.shortest_path_length(comment_tree_nx, 0)

        depth_to_nodecount = collections.defaultdict(int)

        for k, v in node_to_depth.items():
            depth_to_nodecount[v] += 1

        comment_tree_hirsch = max(node_to_depth.values())
        while True:
            if depth_to_nodecount[comment_tree_hirsch] >= comment_tree_hirsch:
                break
            else:
                comment_tree_hirsch -= 1

    return comment_tree_hirsch 

def calculate_max_depth_over_max_width(comment_tree):
    comment_tree_nx = nx.from_scipy_sparse_matrix(comment_tree, create_using=nx.Graph())

    if len(comment_tree_nx) == 0:
        max_depth_over_max_width = 0.0
    else:
        node_to_depth = nx.shortest_path_length(comment_tree_nx, 0)
        depth_to_nodecount = collections.defaultdict(int)

        for k, v in node_to_depth.items():
            depth_to_nodecount[v] += 1

        max_depth = max(node_to_depth.values())
        max_width = max(depth_to_nodecount.values())

        max_depth_over_max_width = max_depth/max_width

    return max_depth_over_max_width 

def test_differential_operator(self, n_vertices=98):
        r"""The Laplacian must always be the divergence of the gradient,
        whether the Laplacian is combinatorial or normalized, and whether the
        graph is directed or weighted."""
        def test_incidence_nx(graph):
            r"""Test that the incidence matrix corresponds to NetworkX."""
            incidence_pg = np.sign(graph.D.toarray())
            G = nx.OrderedDiGraph if graph.is_directed() else nx.OrderedGraph
            graph_nx = nx.from_scipy_sparse_matrix(graph.W, create_using=G)
            incidence_nx = nx.incidence_matrix(graph_nx, oriented=True)
            np.testing.assert_equal(incidence_pg, incidence_nx.toarray())
        for graph in [graphs.Graph(np.zeros((n_vertices, n_vertices))),
                      graphs.Graph(np.identity(n_vertices)),
                      graphs.Graph([[0, 0.8], [0.8, 0]]),
                      graphs.Graph([[1.3, 0], [0.4, 0.5]]),
                      graphs.ErdosRenyi(n_vertices, directed=False, seed=42),
                      graphs.ErdosRenyi(n_vertices, directed=True, seed=42)]:
            for lap_type in ['combinatorial', 'normalized']:
                graph.compute_laplacian(lap_type)
                graph.compute_differential_operator()
                L = graph.D.dot(graph.D.T)
                np.testing.assert_allclose(L.toarray(), graph.L.toarray())
                test_incidence_nx(graph) 

def test_from_scipy_sparse_matrix_parallel_edges(self):
        """Tests that the :func:`networkx.from_scipy_sparse_matrix` function
        interprets integer weights as the number of parallel edges when
        creating a multigraph.

        """
        A = sparse.csr_matrix([[1, 1], [1, 2]])
        # First, with a simple graph, each integer entry in the adjacency
        # matrix is interpreted as the weight of a single edge in the graph.
        expected = nx.DiGraph()
        edges = [(0, 0), (0, 1), (1, 0)]
        expected.add_weighted_edges_from([(u, v, 1) for (u, v) in edges])
        expected.add_edge(1, 1, weight=2)
        actual = nx.from_scipy_sparse_matrix(A, parallel_edges=True,
                                             create_using=nx.DiGraph())
        assert_graphs_equal(actual, expected)
        actual = nx.from_scipy_sparse_matrix(A, parallel_edges=False,
                                             create_using=nx.DiGraph())
        assert_graphs_equal(actual, expected)
        # Now each integer entry in the adjacency matrix is interpreted as the
        # number of parallel edges in the graph if the appropriate keyword
        # argument is specified.
        edges = [(0, 0), (0, 1), (1, 0), (1, 1), (1, 1)]
        expected = nx.MultiDiGraph()
        expected.add_weighted_edges_from([(u, v, 1) for (u, v) in edges])
        actual = nx.from_scipy_sparse_matrix(A, parallel_edges=True,
                                             create_using=nx.MultiDiGraph())
        assert_graphs_equal(actual, expected)
        expected = nx.MultiDiGraph()
        expected.add_edges_from(set(edges), weight=1)
        # The sole self-loop (edge 0) on vertex 1 should have weight 2.
        expected[1][1][0]['weight'] = 2
        actual = nx.from_scipy_sparse_matrix(A, parallel_edges=False,
                                             create_using=nx.MultiDiGraph())
        assert_graphs_equal(actual, expected) 

def test_shape(self):
        "Conversion from non-square sparse array."
        A = sp.sparse.lil_matrix([[1, 2, 3], [4, 5, 6]])
        assert_raises(nx.NetworkXError, nx.from_scipy_sparse_matrix, A) 

def identity_conversion(self, G, A, create_using):
        GG = nx.from_scipy_sparse_matrix(A, create_using=create_using)
        self.assert_isomorphic(G, GG)

        GW = nx.to_networkx_graph(A, create_using=create_using)
        self.assert_isomorphic(G, GW)

        GI = create_using.__class__(A)
        self.assert_isomorphic(G, GI)

        ACSR = A.tocsr()
        GI = create_using.__class__(ACSR)
        self.assert_isomorphic(G, GI)

        ACOO = A.tocoo()
        GI = create_using.__class__(ACOO)
        self.assert_isomorphic(G, GI)

        ACSC = A.tocsc()
        GI = create_using.__class__(ACSC)
        self.assert_isomorphic(G, GI)

        AD = A.todense()
        GI = create_using.__class__(AD)
        self.assert_isomorphic(G, GI)

        AA = A.toarray()
        GI = create_using.__class__(AA)
        self.assert_isomorphic(G, GI) 

def test_symmetric(self):
        """Tests that a symmetric matrix has edges added only once to an
        undirected multigraph when using
        :func:`networkx.from_scipy_sparse_matrix`.

        """
        A = sparse.csr_matrix([[0, 1], [1, 0]])
        G = nx.from_scipy_sparse_matrix(A, create_using=nx.MultiGraph())
        expected = nx.MultiGraph()
        expected.add_edge(0, 1, weight=1)
        assert_graphs_equal(G, expected) 

def test_symmetric(self):
        """Tests that a symmetric matrix has edges added only once to an
        undirected multigraph when using
        :func:`networkx.from_scipy_sparse_matrix`.

        """
        A = sparse.csr_matrix([[0, 1], [1, 0]])
        G = nx.from_scipy_sparse_matrix(A, create_using=nx.MultiGraph)
        expected = nx.MultiGraph()
        expected.add_edge(0, 1, weight=1)
        assert_graphs_equal(G, expected) 

def draw_adjacency_graph(adjacency_matrix,
                         node_color=None,
                         size=10,
                         layout='graphviz',
                         prog='neato',
                         node_size=80,
                         colormap='autumn'):
    """draw_adjacency_graph."""
    graph = nx.from_scipy_sparse_matrix(adjacency_matrix)

    plt.figure(figsize=(size, size))
    plt.grid(False)
    plt.axis('off')

    if layout == 'graphviz':
        pos = nx.graphviz_layout(graph, prog=prog)
    else:
        pos = nx.spring_layout(graph)

    if len(node_color) == 0:
        node_color = 'gray'
    nx.draw_networkx_nodes(graph, pos,
                           node_color=node_color,
                           alpha=0.6,
                           node_size=node_size,
                           cmap=plt.get_cmap(colormap))
    nx.draw_networkx_edges(graph, pos, alpha=0.5)
    plt.show()


# draw a whole set of graphs:: 

def test_from_scipy_sparse_matrix_parallel_edges(self):
        """Tests that the :func:`networkx.from_scipy_sparse_matrix` function
        interprets integer weights as the number of parallel edges when
        creating a multigraph.

        """
        A = sparse.csr_matrix([[1, 1], [1, 2]])
        # First, with a simple graph, each integer entry in the adjacency
        # matrix is interpreted as the weight of a single edge in the graph.
        expected = nx.DiGraph()
        edges = [(0, 0), (0, 1), (1, 0)]
        expected.add_weighted_edges_from([(u, v, 1) for (u, v) in edges])
        expected.add_edge(1, 1, weight=2)
        actual = nx.from_scipy_sparse_matrix(A, parallel_edges=True,
                                             create_using=nx.DiGraph)
        assert_graphs_equal(actual, expected)
        actual = nx.from_scipy_sparse_matrix(A, parallel_edges=False,
                                             create_using=nx.DiGraph)
        assert_graphs_equal(actual, expected)
        # Now each integer entry in the adjacency matrix is interpreted as the
        # number of parallel edges in the graph if the appropriate keyword
        # argument is specified.
        edges = [(0, 0), (0, 1), (1, 0), (1, 1), (1, 1)]
        expected = nx.MultiDiGraph()
        expected.add_weighted_edges_from([(u, v, 1) for (u, v) in edges])
        actual = nx.from_scipy_sparse_matrix(A, parallel_edges=True,
                                             create_using=nx.MultiDiGraph)
        assert_graphs_equal(actual, expected)
        expected = nx.MultiDiGraph()
        expected.add_edges_from(set(edges), weight=1)
        # The sole self-loop (edge 0) on vertex 1 should have weight 2.
        expected[1][1][0]['weight'] = 2
        actual = nx.from_scipy_sparse_matrix(A, parallel_edges=False,
                                             create_using=nx.MultiDiGraph)
        assert_graphs_equal(actual, expected) 

def test_shape(self):
        "Conversion from non-square sparse array."
        A = sp.sparse.lil_matrix([[1, 2, 3], [4, 5, 6]])
        assert_raises(nx.NetworkXError, nx.from_scipy_sparse_matrix, A) 

def identity_conversion(self, G, A, create_using):
        GG = nx.from_scipy_sparse_matrix(A, create_using=create_using)
        self.assert_isomorphic(G, GG)

        GW = nx.to_networkx_graph(A, create_using=create_using)
        self.assert_isomorphic(G, GW)

        GI = nx.empty_graph(0, create_using).__class__(A)
        self.assert_isomorphic(G, GI)

        ACSR = A.tocsr()
        GI = nx.empty_graph(0, create_using).__class__(ACSR)
        self.assert_isomorphic(G, GI)

        ACOO = A.tocoo()
        GI = nx.empty_graph(0, create_using).__class__(ACOO)
        self.assert_isomorphic(G, GI)

        ACSC = A.tocsc()
        GI = nx.empty_graph(0, create_using).__class__(ACSC)
        self.assert_isomorphic(G, GI)

        AD = A.todense()
        GI = nx.empty_graph(0, create_using).__class__(AD)
        self.assert_isomorphic(G, GI)

        AA = A.toarray()
        GI = nx.empty_graph(0, create_using).__class__(AA)
        self.assert_isomorphic(G, GI) 

def test_symmetric(self):
        """Tests that a symmetric matrix has edges added only once to an
        undirected multigraph when using
        :func:`networkx.from_scipy_sparse_matrix`.

        """
        A = sparse.csr_matrix([[0, 1], [1, 0]])
        G = nx.from_scipy_sparse_matrix(A, create_using=nx.MultiGraph())
        expected = nx.MultiGraph()
        expected.add_edge(0, 1, weight=1)
        assert_graphs_equal(G, expected) 

def test_from_scipy_sparse_matrix_parallel_edges(self):
        """Tests that the :func:`networkx.from_scipy_sparse_matrix` function
        interprets integer weights as the number of parallel edges when
        creating a multigraph.

        """
        A = sparse.csr_matrix([[1, 1], [1, 2]])
        # First, with a simple graph, each integer entry in the adjacency
        # matrix is interpreted as the weight of a single edge in the graph.
        expected = nx.DiGraph()
        edges = [(0, 0), (0, 1), (1, 0)]
        expected.add_weighted_edges_from([(u, v, 1) for (u, v) in edges])
        expected.add_edge(1, 1, weight=2)
        actual = nx.from_scipy_sparse_matrix(A, parallel_edges=True,
                                             create_using=nx.DiGraph())
        assert_graphs_equal(actual, expected)
        actual = nx.from_scipy_sparse_matrix(A, parallel_edges=False,
                                             create_using=nx.DiGraph())
        assert_graphs_equal(actual, expected)
        # Now each integer entry in the adjacency matrix is interpreted as the
        # number of parallel edges in the graph if the appropriate keyword
        # argument is specified.
        edges = [(0, 0), (0, 1), (1, 0), (1, 1), (1, 1)]
        expected = nx.MultiDiGraph()
        expected.add_weighted_edges_from([(u, v, 1) for (u, v) in edges])
        actual = nx.from_scipy_sparse_matrix(A, parallel_edges=True,
                                             create_using=nx.MultiDiGraph())
        assert_graphs_equal(actual, expected)
        expected = nx.MultiDiGraph()
        expected.add_edges_from(set(edges), weight=1)
        # The sole self-loop (edge 0) on vertex 1 should have weight 2.
        expected[1][1][0]['weight'] = 2
        actual = nx.from_scipy_sparse_matrix(A, parallel_edges=False,
                                             create_using=nx.MultiDiGraph())
        assert_graphs_equal(actual, expected) 

def test_shape(self):
        "Conversion from non-square sparse array."
        A = sp.sparse.lil_matrix([[1,2,3],[4,5,6]])
        assert_raises(nx.NetworkXError, nx.from_scipy_sparse_matrix, A) 

def identity_conversion(self, G, A, create_using):
        GG = nx.from_scipy_sparse_matrix(A, create_using=create_using)
        self.assert_equal(G, GG)

        GW = nx.to_networkx_graph(A, create_using=create_using)
        self.assert_equal(G, GW)

        GI = create_using.__class__(A)
        self.assert_equal(G, GI)

        ACSR = A.tocsr()
        GI = create_using.__class__(ACSR)
        self.assert_equal(G, GI)

        ACOO = A.tocoo()
        GI = create_using.__class__(ACOO)
        self.assert_equal(G, GI)

        ACSC = A.tocsc()
        GI = create_using.__class__(ACSC)
        self.assert_equal(G, GI)

        AD = A.todense()
        GI = create_using.__class__(AD)
        self.assert_equal(G, GI)

        AA = A.toarray()
        GI = create_using.__class__(AA)
        self.assert_equal(G, GI) 

def test_empty_graph(self, n_vertices=11):
        """Empty graphs have either no edge, or self-loops only. The Laplacian
        doesn't see self-loops, as the gradient on those edges is always zero.
        """
        adjacencies = [
            np.zeros((n_vertices, n_vertices)),
            np.identity(n_vertices),
        ]
        for adjacency, n_edges in zip(adjacencies, [0, n_vertices]):
            graph = graphs.Graph(adjacency)
            self.assertEqual(graph.n_vertices, n_vertices)
            self.assertEqual(graph.n_edges, n_edges)
            self.assertEqual(graph.W.nnz, n_edges)
            for laplacian in ['combinatorial', 'normalized']:
                graph.compute_laplacian(laplacian)
                self.assertEqual(graph.L.nnz, 0)
                sources, targets, weights = graph.get_edge_list()
                self.assertEqual(len(sources), n_edges)
                self.assertEqual(len(targets), n_edges)
                self.assertEqual(len(weights), n_edges)
                graph.compute_differential_operator()
                self.assertEqual(graph.D.nnz, 0)
                graph.compute_fourier_basis()
                np.testing.assert_allclose(graph.U, np.identity(n_vertices))
                np.testing.assert_allclose(graph.e, np.zeros(n_vertices))
            # NetworkX uses the same conventions.
            G = nx.from_scipy_sparse_matrix(graph.W)
            self.assertEqual(nx.laplacian_matrix(G).nnz, 0)
            self.assertEqual(nx.normalized_laplacian_matrix(G).nnz, 0)
            self.assertEqual(nx.incidence_matrix(G).nnz, 0) 

def jaccard_coeff(self):
    """Computes Jaccard coefficients."""
    graph = nx.from_scipy_sparse_matrix(self.adj_matrix)
    coeffs = nx.jaccard_coefficient(graph)
    return coeffs 

def adamic_adar(self):
    """Computes adamic adar scores."""
    graph = nx.from_scipy_sparse_matrix(self.adj_matrix)
    scores = nx.adamic_adar_index(graph)
    return scores 

def get_stationary_distribution_directed(adjacency_matrix, rho):

    graph_nx = nx.from_scipy_sparse_matrix(adjacency_matrix, create_using=nx.DiGraph())

    stationary_distribution = pagerank_scipy(graph_nx,
                                             alpha=1-rho,
                                             personalization=None,
                                             max_iter=200,
                                             tol=1.0e-7,
                                             weight="weight",
                                             dangling=None)

    stationary_distribution = np.array([stationary_distribution[k] for k in sorted(stationary_distribution.keys())])

    return stationary_distribution 

def louvain(adjacency_matrix):
    """
    Performs community embedding using the LOUVAIN method.

    Introduced in: Blondel, V. D., Guillaume, J. L., Lambiotte, R., & Lefebvre, E. (2008).
                   Fast unfolding of communities in large networks.
                   Journal of Statistical Mechanics: Theory and Experiment, 2008(10), P10008.

    Inputs:  - A in R^(nxn): Adjacency matrix of an undirected network represented as a SciPy Sparse COOrdinate matrix.

    Outputs: - X in R^(nxC_n): The latent space embedding represented as a SciPy Sparse COOrdinate matrix.
    """
    # Convert to networkx undirected graph.
    adjacency_matrix = nx.from_scipy_sparse_matrix(adjacency_matrix, create_using=nx.Graph())

    # Call LOUVAIN algorithm to calculate a hierarchy of communities.
    tree = community.generate_dendogram(adjacency_matrix, part_init=None)

    # Embed communities
    row = list()
    col = list()
    append_row = row.append
    append_col = col.append

    community_counter = 0
    for i in range(len(tree)):
        partition = community.partition_at_level(tree, i)
        for n, c in partition.items():
            append_row(n)
            append_col(community_counter + c)

        community_counter += max(partition.values()) + 1

    row = np.array(row)
    col = np.array(col)
    data = np.ones(row.size, dtype=np.float64)

    louvain_features = sparse.coo_matrix((data, (row, col)), shape=(len(partition.keys()), community_counter),
                                         dtype=np.float64)

    return louvain_features 

def reddit_to_networkx(dirpath):
    print("Loading graph data")
    coo_adj = scipy.sparse.load_npz(os.path.join(dirpath, edge_file_name))
    G = nx.from_scipy_sparse_matrix(coo_adj)

    print("Loading node feature and label")
    # node feature, edge label
    reddit_data = numpy.load(os.path.join(dirpath, feat_file_name))
    G.graph['x'] = reddit_data['feature'].astype(numpy.float32)
    G.graph['y'] = reddit_data['label'].astype(numpy.int32)

    G.graph['label_num'] = 41
    # G = nx.convert_node_labels_to_integers(G)
    print("Finish loading graph: {}".format(dirpath))
    return G 

def reduce_graph(self, adj):
        # g = nx.from_scipy_sparse_matrix(adj)
        n_nodes, n_edges, e_froms, e_tos = self.__CtypeAdj(adj)
        reduced_node = (ctypes.c_int * (n_nodes))()
        new_n_nodes = ctypes.c_int()
        new_n_edges = ctypes.c_int()
        reduced_xadj = (ctypes.c_int * (n_nodes+1))()
        reduced_adjncy = (ctypes.c_int * (2*n_edges))()
        mapping = (ctypes.c_int * (n_nodes))()
        reverse_mapping = (ctypes.c_int * (n_nodes))()
        crt_is_size = self.lib.Reduce(n_nodes, n_edges, e_froms, e_tos, reduced_node,
                                      ctypes.byref(new_n_nodes), ctypes.byref(new_n_edges),
                                      reduced_xadj, reduced_adjncy, mapping, reverse_mapping)
        # crt_is_size = self.lib.Reduce(n_nodes, n_edges, e_froms, e_tos, reduced_node)
        new_n_nodes = new_n_nodes.value
        new_n_edges = new_n_edges.value
        reduced_node = np.asarray(reduced_node[:])
        reduced_xadj = np.asarray(reduced_xadj[:])
        reduced_xadj = reduced_xadj[:new_n_nodes+1]
        reduced_adjncy = np.asarray(reduced_adjncy[:])
        reduced_adjncy = reduced_adjncy[:new_n_edges]
        mapping = np.asarray(mapping[:])
        reverse_mapping = np.asarray(reverse_mapping[:])
        reverse_mapping = reverse_mapping[:new_n_nodes]
        reduced_adj = sp.csr_matrix((np.ones(new_n_edges), reduced_adjncy, reduced_xadj), shape=[new_n_nodes, new_n_nodes])
        return reduced_node, reduced_adj, mapping, reverse_mapping, crt_is_size
        # return reduced_node[:], crt_is_size 

def summarize(self, text, length=5, weighting='frequency', norm=None):
        """
        Implements the TextRank summarization algorithm, which follows closely to the PageRank algorithm for ranking
        web pages.

        :param text: a string of text to be summarized, path to a text file, or URL starting with http
        :param length: the length of the output summary; either a number of sentences (e.g. 5) or a percentage
        of the original document (e.g. 0.5)
        :param weighting: 'frequency', 'binary' or 'tfidf' weighting of sentence terms ('frequency' by default)
        :param norm: if 'l1' or 'l2', normalizes words by the length of their associated sentence to "down-weight"
        the voting power of long sentences (None by default)
        :return: list of sentences for the summary
        """

        text = self._parse_input(text)

        sentences, unprocessed_sentences = self._tokenizer.tokenize_sentences(text)

        length = self._parse_summary_length(length, len(sentences))
        if length == len(sentences):
            return unprocessed_sentences

        # Compute the word frequency matrix. If norm is set to 'l1' or 'l2' then words are normalized
        # by the length of their associated sentences (such that each vector of sentence terms sums to 1).
        word_matrix = self._compute_matrix(sentences, weighting=weighting, norm=norm)

        # Build the similarity graph by calculating the number of overlapping words between all
        # combinations of sentences.
        similarity_matrix = (word_matrix * word_matrix.T)

        similarity_graph = networkx.from_scipy_sparse_matrix(similarity_matrix)
        scores = networkx.pagerank(similarity_graph)

        ranked_sentences = sorted(
            ((score, ndx) for ndx, score in scores.items()), reverse=True
        )

        top_sentences = [ranked_sentences[i][1] for i in range(length)]
        top_sentences.sort()

        return [unprocessed_sentences[i] for i in top_sentences] 

def mat_to_nxG(mat):
    g = nx.from_scipy_sparse_matrix(mat)
    return g