Python networkx.average_clustering() Examples

def avg_transitivity(graph, communities, **kwargs):
    """Average transitivity.

    The average transitivity of a community is defined the as the average clustering coefficient of its nodes w.r.t. their connection within the community itself.

    :param graph: a networkx/igraph object
    :param communities: NodeClustering object
    :param summary: boolean. If **True** it is returned an aggregated score for the partition is returned, otherwise individual-community ones. Default **True**.
    :return: If **summary==True** a FitnessResult object, otherwise a list of floats.

    Example:

    >>> from cdlib.algorithms import louvain
    >>> from cdlib import evaluation
    >>> g = nx.karate_club_graph()
    >>> communities = louvain(g)
    >>> scd = evaluation.avg_transitivity(g,communities)
    """

    return __quality_indexes(graph, communities,
                             lambda graph, coms: nx.average_clustering(nx.subgraph(graph, coms)),
                             **kwargs) 

def test_k5(self):
        G = nx.complete_graph(5)
        assert_equal(list(nx.clustering(G, weight='weight').values()), [1, 1, 1, 1, 1])
        assert_equal(nx.average_clustering(G, weight='weight'), 1)
        G.remove_edge(1, 2)
        assert_equal(list(nx.clustering(G, weight='weight').values()),
                     [5. / 6., 1.0, 1.0, 5. / 6., 5. / 6.])
        assert_equal(nx.clustering(G, [1, 4], weight='weight'), {1: 1.0, 4: 0.83333333333333337}) 

def test_complete():
    G = nx.complete_graph(5)
    assert_equal(average_clustering(G, trials=int(len(G)/2)), 1)
    G = nx.complete_graph(7)
    assert_equal(average_clustering(G, trials=int(len(G)/2)), 1) 

def test_empty():
    G = nx.empty_graph(5)
    assert_equal(average_clustering(G, trials=int(len(G)/2)), 0) 

def test_dodecahedral():
    # Actual coefficient is 0
    G = nx.dodecahedral_graph()
    assert_equal(average_clustering(G, trials=int(len(G)/2)),
                 nx.average_clustering(G)) 

def test_petersen():
    # Actual coefficient is 0
    G = nx.petersen_graph()
    assert_equal(average_clustering(G, trials=int(len(G)/2)),
                 nx.average_clustering(G)) 

def test_average_clustering():
    G = nx.cycle_graph(3)
    G.add_edge(2, 3)
    assert_equal(nx.average_clustering(G), (1 + 1 + 1 / 3.0) / 4.0)
    assert_equal(nx.average_clustering(G, count_zeros=True), (1 + 1 + 1 / 3.0) / 4.0)
    assert_equal(nx.average_clustering(G, count_zeros=False), (1 + 1 + 1 / 3.0) / 3.0) 

def test_k5(self):
        G = nx.complete_graph(5)
        assert_equal(list(nx.clustering(G).values()), [1, 1, 1, 1, 1])
        assert_equal(nx.average_clustering(G), 1)
        G.remove_edge(1, 2)
        assert_equal(list(nx.clustering(G).values()),
                     [5. / 6., 1.0, 1.0, 5. / 6., 5. / 6.])
        assert_equal(nx.clustering(G, [1, 4]), {1: 1.0, 4: 0.83333333333333337}) 

def test_k5(self):
        G = nx.complete_graph(5)
        assert_equal(list(nx.clustering(G, weight='weight').values()), [1, 1, 1, 1, 1])
        assert_equal(nx.average_clustering(G, weight='weight'), 1)
        G.remove_edge(1, 2)
        assert_equal(list(nx.clustering(G, weight='weight').values()),
                     [5. / 6., 1.0, 1.0, 5. / 6., 5. / 6.])
        assert_equal(nx.clustering(G, [1, 4], weight='weight'), {1: 1.0, 4: 0.83333333333333337}) 

def test_complete():
    G = nx.complete_graph(5)
    assert_equal(average_clustering(G, trials=int(len(G) / 2)), 1)
    G = nx.complete_graph(7)
    assert_equal(average_clustering(G, trials=int(len(G) / 2)), 1) 

def test_dodecahedral():
    # Actual coefficient is 0
    G = nx.dodecahedral_graph()
    assert_equal(average_clustering(G, trials=int(len(G) / 2)),
                 nx.average_clustering(G)) 

def test_tetrahedral():
    # Actual coefficient is 1
    G = nx.tetrahedral_graph()
    assert_equal(average_clustering(G, trials=int(len(G) / 2)),
                 nx.average_clustering(G)) 

def test_petersen_seed():
    # Actual coefficient is 0
    G = nx.petersen_graph()
    assert_equal(average_clustering(G, trials=int(len(G) / 2), seed=1),
                 nx.average_clustering(G)) 

def test_petersen():
    # Actual coefficient is 0
    G = nx.petersen_graph()
    assert_equal(average_clustering(G, trials=int(len(G) / 2)),
                 nx.average_clustering(G)) 

def test_average_clustering():
    G = nx.cycle_graph(3)
    G.add_edge(2, 3)
    assert_equal(nx.average_clustering(G), (1 + 1 + 1 / 3.0) / 4.0)
    assert_equal(nx.average_clustering(G, count_zeros=True), (1 + 1 + 1 / 3.0) / 4.0)
    assert_equal(nx.average_clustering(G, count_zeros=False), (1 + 1 + 1 / 3.0) / 3.0) 

def plot_clustering_coefficient(_g, _plot_img, interval=30):
    """Plot the clustering coefficient transition
    :param _g: Transaction graph
    :param _plot_img: Output image file
    :param interval: Simulation step interval for plotting
    (it takes too much time to compute clustering coefficient)
    :return:
    """
    date_list = get_date_list(_g)

    gg = nx.Graph()
    edges = defaultdict(list)
    for k, v in nx.get_edge_attributes(_g, "date").items():
        e = (k[0], k[1])
        edges[v].append(e)

    sample_dates = list()
    values = list()
    for i, t in enumerate(date_list):
        gg.add_edges_from(edges[t])
        if i % interval == 0:
            v = nx.average_clustering(gg) if gg.number_of_nodes() else 0.0
            sample_dates.append(t)
            values.append(v)
            print("Clustering coefficient at %s: %f" % (str(t), v))

    plt.figure(figsize=(16, 12))
    plt.clf()
    plt.plot(sample_dates, values, 'bo-')
    plt.title("Clustering Coefficient Transition")
    plt.xlabel("date")
    plt.ylabel("Clustering Coefficient")
    plt.savefig(_plot_img) 

def test_k5(self):
        G = nx.complete_graph(5, create_using=nx.DiGraph())
        assert_equal(list(nx.clustering(G, weight='weight').values()), [1, 1, 1, 1, 1])
        assert_equal(nx.average_clustering(G, weight='weight'), 1)
        G.remove_edge(1, 2)
        assert_equal(list(nx.clustering(G, weight='weight').values()),
                     [11. / 12., 1.0, 1.0, 11. / 12., 11. / 12.])
        assert_equal(nx.clustering(G, [1, 4], weight='weight'), {1: 1.0, 4: 11. /12.})
        G.remove_edge(2, 1)
        assert_equal(list(nx.clustering(G, weight='weight').values()),
                     [5. / 6., 1.0, 1.0, 5. / 6., 5. / 6.])
        assert_equal(nx.clustering(G, [1, 4], weight='weight'), {1: 1.0, 4: 0.83333333333333337}) 

def test_k5(self):
        G = nx.complete_graph(5, create_using=nx.DiGraph())
        assert_equal(list(nx.clustering(G).values()), [1, 1, 1, 1, 1])
        assert_equal(nx.average_clustering(G), 1)
        G.remove_edge(1, 2)
        assert_equal(list(nx.clustering(G).values()),
                     [11. / 12., 1.0, 1.0, 11. / 12., 11. / 12.])
        assert_equal(nx.clustering(G, [1, 4]), {1: 1.0, 4: 11. /12.})
        G.remove_edge(2, 1)
        assert_equal(list(nx.clustering(G).values()),
                     [5. / 6., 1.0, 1.0, 5. / 6., 5. / 6.])
        assert_equal(nx.clustering(G, [1, 4]), {1: 1.0, 4: 0.83333333333333337}) 

def test_random_reference():
    G = nx.connected_watts_strogatz_graph(50, 6, 0.1, seed=rng)
    Gr = random_reference(G, niter=1, seed=rng)
    C = nx.average_clustering(G)
    Cr = nx.average_clustering(Gr)
    assert_true(C > Cr)

    assert_raises(nx.NetworkXError, random_reference, nx.Graph())
    assert_raises(nx.NetworkXNotImplemented, random_reference, nx.DiGraph())

    H = nx.Graph(((0, 1), (2, 3)))
    Hl = random_reference(H, niter=1, seed=rng) 

def test_complete():
    G = nx.complete_graph(5)
    assert_equal(average_clustering(G, trials=int(len(G)/2)), 1)
    G = nx.complete_graph(7)
    assert_equal(average_clustering(G, trials=int(len(G)/2)), 1) 

def test_empty():
    G = nx.empty_graph(5)
    assert_equal(average_clustering(G, trials=int(len(G)/2)), 0) 

def test_dodecahedral():
    # Actual coefficient is 0
    G = nx.dodecahedral_graph()
    assert_equal(average_clustering(G, trials=int(len(G)/2)),
                 nx.average_clustering(G)) 

def test_petersen():
    # Actual coefficient is 0
    G = nx.petersen_graph()
    assert_equal(average_clustering(G, trials=int(len(G)/2)),
                 nx.average_clustering(G)) 

def test_average_clustering():
    G=nx.cycle_graph(3)
    G.add_edge(2,3)
    assert_equal(nx.average_clustering(G),(1+1+1/3.0)/4.0)
    assert_equal(nx.average_clustering(G,count_zeros=True),(1+1+1/3.0)/4.0)
    assert_equal(nx.average_clustering(G,count_zeros=False),(1+1+1/3.0)/3.0) 

def test_k5(self):
        G = nx.complete_graph(5)
        assert_equal(list(nx.clustering(G).values()),[1, 1, 1, 1, 1])
        assert_equal(nx.average_clustering(G),1)
        G.remove_edge(1,2)
        assert_equal(list(nx.clustering(G).values()),
                     [5./6., 1.0, 1.0, 5./6., 5./6.])
        assert_equal(nx.clustering(G,[1,4]),{1: 1.0, 4: 0.83333333333333337}) 

def test_k5(self):
        G = nx.complete_graph(5)
        assert_equal(list(nx.clustering(G,weight='weight').values()),[1, 1, 1, 1, 1])
        assert_equal(nx.average_clustering(G,weight='weight'),1)
        G.remove_edge(1,2)
        assert_equal(list(nx.clustering(G,weight='weight').values()),
                     [5./6., 1.0, 1.0, 5./6., 5./6.])
        assert_equal(nx.clustering(G,[1,4],weight='weight'),{1: 1.0, 4: 0.83333333333333337}) 

def get_clustering_coeff(edge_list):
    G = nx.from_edgelist(edgelist=edge_list)
    clust_coeff = nx.average_clustering(G)
    # print(nx.number_of_nodes(G), ' : ',clust_coeff)
    return clust_coeff 

def average_clustering(G, nodes=None, weight=None, count_zeros=True):
    r"""Compute the average clustering coefficient for the graph G.

    The clustering coefficient for the graph is the average,

    .. math::

       C = \frac{1}{n}\sum_{v \in G} c_v,

    where :math:`n` is the number of nodes in `G`.

    Parameters
    ----------
    G : graph

    nodes : container of nodes, optional (default=all nodes in G)
       Compute average clustering for nodes in this container.

    weight : string or None, optional (default=None)
       The edge attribute that holds the numerical value used as a weight.
       If None, then each edge has weight 1.

    count_zeros : bool
       If False include only the nodes with nonzero clustering in the average.

    Returns
    -------
    avg : float
       Average clustering

    Examples
    --------
    >>> G=nx.complete_graph(5)
    >>> print(nx.average_clustering(G))
    1.0

    Notes
    -----
    This is a space saving routine; it might be faster
    to use the clustering function to get a list and then take the average.

    Self loops are ignored.

    References
    ----------
    .. [1] Generalizations of the clustering coefficient to weighted
       complex networks by J. Saramäki, M. Kivelä, J.-P. Onnela,
       K. Kaski, and J. Kertész, Physical Review E, 75 027105 (2007).
       http://jponnela.com/web_documents/a9.pdf
    .. [2] Marcus Kaiser,  Mean clustering coefficients: the role of isolated
       nodes and leafs on clustering measures for small-world networks.
       https://arxiv.org/abs/0802.2512
    """
    c = clustering(G, nodes, weight=weight).values()
    if not count_zeros:
        c = [v for v in c if v > 0]
    return sum(c) / len(c) 

def average_clustering(G, nodes=None, weight=None, count_zeros=True):
    r"""Compute the average clustering coefficient for the graph G.

    The clustering coefficient for the graph is the average,

    .. math::

       C = \frac{1}{n}\sum_{v \in G} c_v,

    where `n` is the number of nodes in `G`.

    Parameters
    ----------
    G : graph

    nodes : container of nodes, optional (default=all nodes in G)
       Compute average clustering for nodes in this container.

    weight : string or None, optional (default=None)
       The edge attribute that holds the numerical value used as a weight.
       If None, then each edge has weight 1.

    count_zeros : bool
       If False include only the nodes with nonzero clustering in the average.

    Returns
    -------
    avg : float
       Average clustering

    Examples
    --------
    >>> G=nx.complete_graph(5)
    >>> print(nx.average_clustering(G))
    1.0

    Notes
    -----
    This is a space saving routine; it might be faster
    to use the clustering function to get a list and then take the average.

    Self loops are ignored.

    References
    ----------
    .. [1] Generalizations of the clustering coefficient to weighted
       complex networks by J. Saramäki, M. Kivelä, J.-P. Onnela,
       K. Kaski, and J. Kertész, Physical Review E, 75 027105 (2007).
       http://jponnela.com/web_documents/a9.pdf
    .. [2] Marcus Kaiser,  Mean clustering coefficients: the role of isolated
       nodes and leafs on clustering measures for small-world networks.
       https://arxiv.org/abs/0802.2512
    """
    c = clustering(G, nodes, weight=weight).values()
    if not count_zeros:
        c = [v for v in c if v > 0]
    return sum(c) / len(c) 

def average_clustering(G, nodes=None, weight=None, count_zeros=True):
    r"""Compute the average clustering coefficient for the graph G.

    The clustering coefficient for the graph is the average, 

    .. math::

       C = \frac{1}{n}\sum_{v \in G} c_v,
       
    where `n` is the number of nodes in `G`.

    Parameters
    ----------
    G : graph

    nodes : container of nodes, optional (default=all nodes in G)
       Compute average clustering for nodes in this container. 

    weight : string or None, optional (default=None)
       The edge attribute that holds the numerical value used as a weight.
       If None, then each edge has weight 1.

    count_zeros : bool
       If False include only the nodes with nonzero clustering in the average.

    Returns
    -------
    avg : float
       Average clustering
    
    Examples
    --------
    >>> G=nx.complete_graph(5)
    >>> print(nx.average_clustering(G))
    1.0

    Notes
    -----
    This is a space saving routine; it might be faster
    to use the clustering function to get a list and then take the average.

    Self loops are ignored.

    References
    ----------
    .. [1] Generalizations of the clustering coefficient to weighted 
       complex networks by J. Saramäki, M. Kivelä, J.-P. Onnela, 
       K. Kaski, and J. Kertész, Physical Review E, 75 027105 (2007).  
       http://jponnela.com/web_documents/a9.pdf
    .. [2] Marcus Kaiser,  Mean clustering coefficients: the role of isolated 
       nodes and leafs on clustering measures for small-world networks.
       http://arxiv.org/abs/0802.2512
    """
    c=clustering(G,nodes,weight=weight).values()
    if not count_zeros:
        c = [v for v in c if v > 0]
    return sum(c)/float(len(c))