聚类系数可变无标度网络模型Holme-Kim HK模型

Posted 2020-09-26 bethansy

# -*- coding: cp936 -*-
import random
import networkx as nx
from networkx.generators.classic import empty_graph

def powerlaw_cluster_graph(n, m, p, seed=None):
    """Holme and Kim algorithm for growing graphs with powerlaw
    degree distribution and approximate average clustering.

    Parameters
    ----------
    n : int
        the number of nodes
    m : int
        the number of random edges to add for each new node
    p : float,
        Probability of adding a triangle after adding a random edge
    seed : int, optional
        Seed for random number generator (default=None).

    Notes
    -----
    The average clustering has a hard time getting above a certain
    cutoff that depends on ``m``.  This cutoff is often quite low.  The
    transitivity (fraction of triangles to possible triangles) seems to
    decrease with network size.

    It is essentially the Barabási–Albert (BA) growth model with an
    extra step that each random edge is followed by a chance of
    making an edge to one of its neighbors too (and thus a triangle).

    This algorithm improves on BA in the sense that it enables a
    higher average clustering to be attained if desired.

    It seems possible to have a disconnected graph with this algorithm
    since the initial ``m`` nodes may not be all linked to a new node
    on the first iteration like the BA model.

    Raises
    ------
    NetworkXError
        If ``m`` does not satisfy ``1 <= m <= n`` or ``p`` does not
        satisfy ``0 <= p <= 1``.

    References
    ----------
    .. [1] P. Holme and B. J. Kim,
       "Growing scale-free networks with tunable clustering",
       Phys. Rev. E, 65, 026107, 2002.
    """

    if m < 1 or n < m:
        raise nx.NetworkXError(              "NetworkXError must have m>1 and m<n, m=%d,n=%d"%(m,n))

    if p > 1 or p < 0:
        raise nx.NetworkXError(              "NetworkXError p must be in [0,1], p=%f"%(p))
    if seed is not None:
        random.seed(seed)

    G=empty_graph(m) # add m initial nodes (m0 in barabasi-speak)
    G.name="Powerlaw-Cluster Graph"
    repeated_nodes=G.nodes()  # list of existing nodes to sample from
                           # with nodes repeated once for each adjacent edge
    source=m               # next node is m
    while source<n:        # Now add the other n-1 nodes
        possible_targets = _random_subset(repeated_nodes,m)
        # do one preferential attachment for new node
        target=possible_targets.pop()
        G.add_edge(source,target)
        repeated_nodes.append(target) # add one node to list for each new link
        count=1
        while count<m:  # add m-1 more new links
            if random.random()<p: # clustering step: add triangle
                neighborhood=[nbr for nbr in G.neighbors(target)                                if not G.has_edge(source,nbr)                                and not nbr==source]
                if neighborhood: # if there is a neighbor without a link
                    nbr=random.choice(neighborhood)
                    G.add_edge(source,nbr) # add triangle
                    repeated_nodes.append(nbr)
                    count=count+1
                    continue # go to top of while loop
            # else do preferential attachment step if above fails
            target=possible_targets.pop()
            G.add_edge(source,target)
            repeated_nodes.append(target)
            count=count+1

        repeated_nodes.extend([source]*m)  # add source node to list m times
        source += 1
    return G
def _random_subset(seq,m):
    """ Return m unique elements from seq.

    This differs from random.sample which can return repeated
    elements if seq holds repeated elements.
    :param seq:
    :param m:
    :return:
    """
    targets=set()
    while len(targets)<m:
        x=random.choice(seq)
        targets.add(x)
    return targets
if __name__=="__main__":
    n=input(" the number of nodes:")
    m=input("the number of random edges to add for each new node:")
    p=input("Probability of adding a triangle after adding a random edge:")
    g=powerlaw_cluster_graph(n, m, p, seed=None)
    node = list(g.nodes())
    edge = list(g.edges())
    # with open(‘node.pickle‘, ‘wb‘) as f:
    #    pickle.dump(node, f)
    #with open(‘edge.pickle‘, ‘wb‘) as f:
    #   pickle.dump(edge, f)
    #print(node)
    #print(edge)
    #edge = list(edge)
    fil = open(‘edge.txt‘, ‘w‘)
    for i in edge:
        fil.write(‘{} {}\n‘.format(*i))
    fil.close()

　　生成无标度网络，通过P控制聚类系数