Python Topology.number_of_edges方法代码示例

# 需要导入模块: from fnss.topologies.topology import Topology [as 别名]
# 或者: from fnss.topologies.topology.Topology import number_of_edges [as 别名]
def extended_barabasi_albert_topology(n, m, m0, p, q, seed=None):
    r"""
    Return a random topology using the extended Barabasi-Albert preferential
    attachment model.

    Differently from the original Barabasi-Albert model, this model takes into
    account the presence of local events, such as the addition of new links or
    the rewiring of existing links.

    More precisely, the Barabasi-Albert topology is built as follows. First, a
    topology with *m0* isolated nodes is created. Then, at each step:
    with probability *p* add *m* new links between existing nodes, selected
    with probability:

    .. math::
        \Pi(i) = \frac{deg(i) + 1}{\sum_{v \in V} (deg(v) + 1)}

    with probability *q* rewire *m* links. Each link to be rewired is selected as
    follows: a node i is randomly selected and a link is randomly removed from
    it. The node i is then connected to a new node randomly selected with
    probability :math:`\Pi(i)`,
    with probability :math:`1-p-q` add a new node and attach it to m nodes of
    the existing topology selected with probability :math:`\Pi(i)`

    Repeat the previous step until the topology comprises n nodes in total.

    Parameters
    ----------
    n : int
        Number of nodes
    m : int
        Number of edges to attach from a new node to existing nodes
    m0 : int
        Number of edges initially attached to the network
    p : float
        The probability that new links are added
    q : float
        The probability that existing links are rewired
    seed : int, optional
        Seed for random number generator (default=None).

    Returns
    -------
    G : Topology

    References
    ----------
    .. [1] A. L. Barabasi and R. Albert "Topology of evolving networks: local
       events and universality", Physical Review Letters 85(24), 2000.
    """
    def calc_pi(G):
        """Calculate extended-BA Pi function for all nodes of the graph"""
        degree = dict(G.degree())
        den = float(sum(degree.values()) + G.number_of_nodes())
        return {node: (degree[node] + 1) / den for node in G.nodes()}

    # input parameters
    if n < 1 or m < 1 or m0 < 1:
        raise ValueError('n, m and m0 must be a positive integer')
    if m >= m0:
        raise ValueError('m must be <= m0')
    if n < m0:
        raise ValueError('n must be > m0')
    if p > 1 or p < 0:
        raise ValueError('p must be included between 0 and 1')
    if q > 1 or q < 0:
        raise ValueError('q must be included between 0 and 1')
    if p + q > 1:
        raise ValueError('p + q must be <= 1')
    if seed is not None:
        random.seed(seed)
    G = Topology(type='extended_ba')
    G.name = "ext_ba_topology(%d, %d, %d, %f, %f)" % (n, m, m0, p, q)
    # Step 1: Add m0 isolated nodes
    G.add_nodes_from(range(m0))

    while G.number_of_nodes() < n:
        pi = calc_pi(G)
        r = random.random()

        if r <= p:
            # add m new links with probability p
            n_nodes = G.number_of_nodes()
            n_edges = G.number_of_edges()
            max_n_edges = (n_nodes * (n_nodes - 1)) / 2
            if n_edges + m > max_n_edges:  # cannot add m links
                continue  # rewire or add nodes
            new_links = 0
            while new_links < m:
                u = random_from_pdf(pi)
                v = random_from_pdf(pi)
                if u is not v and not G.has_edge(u, v):
                    G.add_edge(u, v)
                    new_links += 1

        elif r > p and r <= p + q:
            # rewire m links with probability q
            rewired_links = 0
            while rewired_links < m:
                i = random.choice(list(G.nodes()))  # pick up node randomly (uniform)
#.........这里部分代码省略.........