Python networkx.degree_histogram() Examples

def decode_graph(adj, prefix):
    adj = np.asmatrix(adj)
    G = nx.from_numpy_matrix(adj)
    # G.remove_nodes_from(nx.isolates(G))
    print('num of nodes: {}'.format(G.number_of_nodes()))
    print('num of edges: {}'.format(G.number_of_edges()))
    G_deg = nx.degree_histogram(G)
    G_deg_sum = [a * b for a, b in zip(G_deg, range(0, len(G_deg)))]
    print('average degree: {}'.format(sum(G_deg_sum) / G.number_of_nodes()))
    if nx.is_connected(G):
        print('average path length: {}'.format(nx.average_shortest_path_length(G)))
        print('average diameter: {}'.format(nx.diameter(G)))
    G_cluster = sorted(list(nx.clustering(G).values()))
    print('average clustering coefficient: {}'.format(sum(G_cluster) / len(G_cluster)))
    cycle_len = []
    cycle_all = nx.cycle_basis(G, 0)
    for item in cycle_all:
        cycle_len.append(len(item))
    print('cycles', cycle_len)
    print('cycle count', len(cycle_len))
    draw_graph(G, prefix=prefix) 

def decode_graph(adj, prefix):
    adj = np.asmatrix(adj)
    G = nx.from_numpy_matrix(adj)
    # G.remove_nodes_from(nx.isolates(G))
    print('num of nodes: {}'.format(G.number_of_nodes()))
    print('num of edges: {}'.format(G.number_of_edges()))
    G_deg = nx.degree_histogram(G)
    G_deg_sum = [a * b for a, b in zip(G_deg, range(0, len(G_deg)))]
    print('average degree: {}'.format(sum(G_deg_sum) / G.number_of_nodes()))
    if nx.is_connected(G):
        print('average path length: {}'.format(nx.average_shortest_path_length(G)))
        print('average diameter: {}'.format(nx.diameter(G)))
    G_cluster = sorted(list(nx.clustering(G).values()))
    print('average clustering coefficient: {}'.format(sum(G_cluster) / len(G_cluster)))
    cycle_len = []
    cycle_all = nx.cycle_basis(G, 0)
    for item in cycle_all:
        cycle_len.append(len(item))
    print('cycles', cycle_len)
    print('cycle count', len(cycle_len))
    draw_graph(G, prefix=prefix) 

def test_grid_graph(self):
        """grid_graph([n,m]) is a connected simple graph with the
        following properties:
        number_of_nodes = n*m
        degree_histogram = [0,0,4,2*(n+m)-8,(n-2)*(m-2)]
        """
        for n, m in [(3, 5), (5, 3), (4, 5), (5, 4)]:
            dim = [n, m]
            g = nx.grid_graph(dim)
            assert_equal(len(g), n*m)
            assert_equal(nx.degree_histogram(g), [0, 0, 4, 2 * (n + m) - 8,
                                                  (n - 2) * (m - 2)])

        for n, m in [(1, 5), (5, 1)]:
            dim = [n, m]
            g = nx.grid_graph(dim)
            assert_equal(len(g), n*m)
            assert_true(nx.is_isomorphic(g, nx.path_graph(5)))

#        mg = nx.grid_graph([n,m], create_using=MultiGraph())
#        assert_equal(mg.edges(), g.edges()) 

def test_grid_graph(self):
        """grid_graph([n,m]) is a connected simple graph with the
        following properties:
        number_of_nodes = n*m
        degree_histogram = [0,0,4,2*(n+m)-8,(n-2)*(m-2)]
        """
        for n, m in [(3, 5), (5, 3), (4, 5), (5, 4)]:
            dim = [n, m]
            g = nx.grid_graph(dim)
            assert_equal(len(g), n * m)
            assert_equal(nx.degree_histogram(g), [0, 0, 4, 2 * (n + m) - 8,
                                                  (n - 2) * (m - 2)])

        for n, m in [(1, 5), (5, 1)]:
            dim = [n, m]
            g = nx.grid_graph(dim)
            assert_equal(len(g), n * m)
            assert_true(nx.is_isomorphic(g, nx.path_graph(5)))

#        mg = nx.grid_graph([n,m], create_using=MultiGraph())
#        assert_equal(mg.edges(), g.edges()) 

def _compute_rc(G):
    # compute rich club coefficient for all k degrees in G
    deghist = nx.degree_histogram(G)
    total = sum(deghist)
    # number of nodes with degree > k (omit last entry which is zero)
    nks = [total-cs for cs in nx.utils.accumulate(deghist) if total-cs > 1]
    deg=G.degree()
    edge_degrees=sorted(sorted((deg[u],deg[v])) for u,v in G.edges_iter()) 
    ek=G.number_of_edges()
    k1,k2=edge_degrees.pop(0)
    rc={}
    for d,nk in zip(range(len(nks)),nks):         
        while k1 <= d:
            if len(edge_degrees)==0:
                break
            k1,k2=edge_degrees.pop(0)
            ek-=1
        rc[d] = 2.0*ek/(nk*(nk-1))
    return rc 

def _compute_rc(G):
    """Returns the rich-club coefficient for each degree in the graph
    `G`.

    `G` is an undirected graph without multiedges.

    Returns a dictionary mapping degree to rich-club coefficient for
    that degree.

    """
    deghist = nx.degree_histogram(G)
    total = sum(deghist)
    # Compute the number of nodes with degree greater than `k`, for each
    # degree `k` (omitting the last entry, which is zero).
    nks = (total - cs for cs in accumulate(deghist) if total - cs > 1)
    # Create a sorted list of pairs of edge endpoint degrees.
    #
    # The list is sorted in reverse order so that we can pop from the
    # right side of the list later, instead of popping from the left
    # side of the list, which would have a linear time cost.
    edge_degrees = sorted((sorted(map(G.degree, e)) for e in G.edges()),
                          reverse=True)
    ek = G.number_of_edges()
    k1, k2 = edge_degrees.pop()
    rc = {}
    for d, nk in enumerate(nks):
        while k1 <= d:
            if len(edge_degrees) == 0:
                ek = 0
                break
            k1, k2 = edge_degrees.pop()
            ek -= 1
        rc[d] = 2 * ek / (nk * (nk - 1))
    return rc 

def test_degree_distribution(self):
        for n in range(1, 10):
            G = nx.hypercube_graph(n)
            expected_histogram = [0] * n + [2 ** n]
            assert_equal(nx.degree_histogram(G), expected_histogram) 

def get_degree_distribution(edge_list):
    G = nx.from_edgelist(edge_list)
    hist = nx.degree_histogram(G)
    return hist 

def test_degree_distribution(self):
        m, n = 5, 6
        G = nx.grid_2d_graph(m, n)
        expected_histogram = [0, 0, 4, 2 * (m + n) - 8, (m - 2) * (n - 2)]
        assert_equal(nx.degree_histogram(G), expected_histogram) 

def _compute_rc(G):
    """Returns the rich-club coefficient for each degree in the graph
    `G`.

    `G` is an undirected graph without multiedges.

    Returns a dictionary mapping degree to rich-club coefficient for
    that degree.

    """
    deghist = nx.degree_histogram(G)
    total = sum(deghist)
    # Compute the number of nodes with degree greater than `k`, for each
    # degree `k` (omitting the last entry, which is zero).
    nks = (total - cs for cs in accumulate(deghist) if total - cs > 1)
    # Create a sorted list of pairs of edge endpoint degrees.
    #
    # The list is sorted in reverse order so that we can pop from the
    # right side of the list later, instead of popping from the left
    # side of the list, which would have a linear time cost.
    edge_degrees = sorted((sorted(map(G.degree, e)) for e in G.edges()),
                          reverse=True)
    ek = G.number_of_edges()
    k1, k2 = edge_degrees.pop()
    rc = {}
    for d, nk in enumerate(nks):
        while k1 <= d:
            if len(edge_degrees) == 0:
                ek = 0
                break
            k1, k2 = edge_degrees.pop()
            ek -= 1
        rc[d] = 2 * ek / (nk * (nk - 1))
    return rc 

def test_degree_histogram(self):
        assert_equal(nx.degree_histogram(self.G), [1, 1, 1, 1, 1]) 

def test_degree_distribution(self):
        for n in range(1, 10):
            G = nx.hypercube_graph(n)
            expected_histogram = [0] * n + [2 ** n]
            assert_equal(nx.degree_histogram(G), expected_histogram) 

def degree_worker(G):
    return np.array(nx.degree_histogram(G)) 

def test_degree_distribution(self):
        m, n = 5, 6
        G = nx.grid_2d_graph(m, n)
        expected_histogram = [0, 0, 4, 2 * (m + n) - 8, (m - 2) * (n - 2)]
        assert_equal(nx.degree_histogram(G), expected_histogram) 

def test_degree_histogram(self):
        assert_equal(nx.degree_histogram(self.G), [1, 1, 1, 1, 1]) 

def degree_stats(graph_ref_list, graph_pred_list, is_parallel=False):
    ''' Compute the distance between the degree distributions of two unordered sets of graphs.
    Args:
      graph_ref_list, graph_target_list: two lists of networkx graphs to be evaluated
    '''
    sample_ref = []
    sample_pred = []
    # in case an empty graph is generated
    graph_pred_list_remove_empty = [G for G in graph_pred_list if not G.number_of_nodes() == 0]

    prev = datetime.now()
    if is_parallel:
        with concurrent.futures.ProcessPoolExecutor() as executor:
            for deg_hist in executor.map(degree_worker, graph_ref_list):
                sample_ref.append(deg_hist)
        with concurrent.futures.ProcessPoolExecutor() as executor:
            for deg_hist in executor.map(degree_worker, graph_pred_list_remove_empty):
                sample_pred.append(deg_hist)

    else:
        for i in range(len(graph_ref_list)):
            degree_temp = np.array(nx.degree_histogram(graph_ref_list[i]))
            sample_ref.append(degree_temp)
        for i in range(len(graph_pred_list_remove_empty)):
            degree_temp = np.array(nx.degree_histogram(graph_pred_list_remove_empty[i]))
            sample_pred.append(degree_temp)
    print(len(sample_ref),len(sample_pred))
    mmd_dist = mmd.compute_mmd(sample_ref, sample_pred, kernel=mmd.gaussian_emd)
    elapsed = datetime.now() - prev
    if PRINT_TIME:
        print('Time computing degree mmd: ', elapsed)
    return mmd_dist 

def test_degree_histogram(self):
        assert_equal(nx.degree_histogram(self.G), [1,1,1,1,1]) 

def get_degree_hist(graph):
    r"""
    Compute histogram of node degrees for a graph.
    
    :param graph: graph representation in networkx format: nx.from_numpy_matrix(A)
    :return: histogram of degrees
    """
    hist_d = nx.degree_histogram(graph)
    return np.array(hist_d) 

def degree_stats(graph_ref_list, graph_pred_list, is_parallel=False):
    ''' Compute the distance between the degree distributions of two unordered sets of graphs.
    Args:
      graph_ref_list, graph_target_list: two lists of networkx graphs to be evaluated
    '''
    sample_ref = []
    sample_pred = []
    # in case an empty graph is generated
    graph_pred_list_remove_empty = [G for G in graph_pred_list if not G.number_of_nodes() == 0]

    prev = datetime.now()
    if is_parallel:
        with concurrent.futures.ProcessPoolExecutor() as executor:
            for deg_hist in executor.map(degree_worker, graph_ref_list):
                sample_ref.append(deg_hist)
        with concurrent.futures.ProcessPoolExecutor() as executor:
            for deg_hist in executor.map(degree_worker, graph_pred_list_remove_empty):
                sample_pred.append(deg_hist)

    else:
        for i in range(len(graph_ref_list)):
            degree_temp = np.array(nx.degree_histogram(graph_ref_list[i]))
            sample_ref.append(degree_temp)
        for i in range(len(graph_pred_list_remove_empty)):
            degree_temp = np.array(nx.degree_histogram(graph_pred_list_remove_empty[i]))
            sample_pred.append(degree_temp)
    print(len(sample_ref),len(sample_pred))
    mmd_dist = mmd.compute_mmd(sample_ref, sample_pred, kernel=mmd.gaussian_emd)
    elapsed = datetime.now() - prev
    if PRINT_TIME:
        print('Time computing degree mmd: ', elapsed)
    return mmd_dist 

def degree_worker(G):
    return np.array(nx.degree_histogram(G)) 

def Graph_synthetic(seed):
    G = nx.Graph()
    np.random.seed(seed)
    base = np.repeat(np.eye(5), 20, axis=0)
    rand = np.random.randn(100, 5) * 0.05
    node_features = base + rand

    # # print('node features')
    # for i in range(node_features.shape[0]):
    #     print(np.around(node_features[i], decimals=4))

    node_distance_l1 = np.ones((node_features.shape[0], node_features.shape[0]))
    node_distance_np = np.zeros((node_features.shape[0], node_features.shape[0]))
    for i in range(node_features.shape[0]):
        for j in range(node_features.shape[0]):
            if i != j:
                node_distance_l1[i,j] = np.sum(np.abs(node_features[i] - node_features[j]))
                # print('node distance', node_distance_l1[i,j])
                node_distance_np[i, j] = 1 / np.sum(np.abs(node_features[i] - node_features[j]) ** 2)

    print('node distance max', np.max(node_distance_l1))
    print('node distance min', np.min(node_distance_l1))
    node_distance_np_sum = np.sum(node_distance_np, axis=1, keepdims=True)
    embedding_dist = node_distance_np / node_distance_np_sum

    # generate the graph
    average_degree = 9
    for i in range(node_features.shape[0]):
        for j in range(i + 1, embedding_dist.shape[0]):
            p = np.random.rand()
            if p < embedding_dist[i, j] * average_degree:
                G.add_edge(i, j)

    G.remove_nodes_from(nx.isolates(G))
    print('num of nodes', G.number_of_nodes())
    print('num of edges', G.number_of_edges())

    G_deg = nx.degree_histogram(G)
    G_deg_sum = [a * b for a, b in zip(G_deg, range(0, len(G_deg)))]
    print('average degree', sum(G_deg_sum) / G.number_of_nodes())
    print('average path length', nx.average_shortest_path_length(G))
    print('diameter', nx.diameter(G))
    G_cluster = sorted(list(nx.clustering(G).values()))
    print('average clustering coefficient', sum(G_cluster) / len(G_cluster))
    print('Graph generation complete!')
    # node_features = np.concatenate((node_features, np.zeros((1,node_features.shape[1]))),axis=0)

    return G, node_features

# G = Graph_synthetic(10)



# return adj and features from a single graph 

def Graph_synthetic(seed):
    G = nx.Graph()
    np.random.seed(seed)
    base = np.repeat(np.eye(5), 20, axis=0)
    rand = np.random.randn(100, 5) * 0.05
    node_features = base + rand

    # # print('node features')
    # for i in range(node_features.shape[0]):
    #     print(np.around(node_features[i], decimals=4))

    node_distance_l1 = np.ones((node_features.shape[0], node_features.shape[0]))
    node_distance_np = np.zeros((node_features.shape[0], node_features.shape[0]))
    for i in range(node_features.shape[0]):
        for j in range(node_features.shape[0]):
            if i != j:
                node_distance_l1[i,j] = np.sum(np.abs(node_features[i] - node_features[j]))
                # print('node distance', node_distance_l1[i,j])
                node_distance_np[i, j] = 1 / np.sum(np.abs(node_features[i] - node_features[j]) ** 2)

    print('node distance max', np.max(node_distance_l1))
    print('node distance min', np.min(node_distance_l1))
    node_distance_np_sum = np.sum(node_distance_np, axis=1, keepdims=True)
    embedding_dist = node_distance_np / node_distance_np_sum

    # generate the graph
    average_degree = 9
    for i in range(node_features.shape[0]):
        for j in range(i + 1, embedding_dist.shape[0]):
            p = np.random.rand()
            if p < embedding_dist[i, j] * average_degree:
                G.add_edge(i, j)

    G.remove_nodes_from(nx.isolates(G))
    print('num of nodes', G.number_of_nodes())
    print('num of edges', G.number_of_edges())

    G_deg = nx.degree_histogram(G)
    G_deg_sum = [a * b for a, b in zip(G_deg, range(0, len(G_deg)))]
    print('average degree', sum(G_deg_sum) / G.number_of_nodes())
    print('average path length', nx.average_shortest_path_length(G))
    print('diameter', nx.diameter(G))
    G_cluster = sorted(list(nx.clustering(G).values()))
    print('average clustering coefficient', sum(G_cluster) / len(G_cluster))
    print('Graph generation complete!')
    # node_features = np.concatenate((node_features, np.zeros((1,node_features.shape[1]))),axis=0)

    return G, node_features

# G = Graph_synthetic(10)



# return adj and features from a single graph