生成具有一定程度分布的图形？

Question

我试图生成一个具有小世界属性的随机图(展示幂律分布).我刚开始使用networkx软件包,发现它提供了各种随机图生成.有人能告诉我是否有可能生成一个图形,其中给定节点的度数遵循伽马分布(在R中或使用python的networkx包)？

Answer 1

如果你想使用配置模型,这样的东西应该在NetworkX中工作:

import random 
import networkx as nx
z=[int(random.gammavariate(alpha=9.0,beta=2.0)) for i in range(100)]
G=nx.configuration_model(z)

您可能需要根据伽马分布中的参数调整序列z的平均值.z也不需要是图形(你会得到一个多图),但它确实需要一个偶数总和,所以你可能需要尝试一些随机序列(或加1)...

关于configuration_model的NetworkX文档说明给出了另一个示例,一个参考以及如何删除并行边和自循环:

Notes
-----
As described by Newman [1]_.

A non-graphical degree sequence (not realizable by some simple
graph) is allowed since this function returns graphs with self
loops and parallel edges.  An exception is raised if the degree
sequence does not have an even sum.

This configuration model construction process can lead to
duplicate edges and loops.  You can remove the self-loops and
parallel edges (see below) which will likely result in a graph
that doesn't have the exact degree sequence specified.  This
"finite-size effect" decreases as the size of the graph increases.

References
----------
.. [1] M.E.J. Newman, "The structure and function
       of complex networks", SIAM REVIEW 45-2, pp 167-256, 2003.

Examples
--------
>>> from networkx.utils import powerlaw_sequence
>>> z=nx.create_degree_sequence(100,powerlaw_sequence)
>>> G=nx.configuration_model(z)

To remove parallel edges:

>>> G=nx.Graph(G)

To remove self loops:

>>> G.remove_edges_from(G.selfloop_edges())

以下示例类似于http://networkx.lanl.gov/examples/drawing/degree_histogram.html上的示例,该示例生成的图形包括最大连接组件的图形布局:

#!/usr/bin/env python
import random
import matplotlib.pyplot as plt
import networkx as nx

def seq(n):
    return [random.gammavariate(alpha=2.0,beta=1.0) for i in range(100)]    
z=nx.create_degree_sequence(100,seq)
nx.is_valid_degree_sequence(z)
G=nx.configuration_model(z)  # configuration model

degree_sequence=sorted(nx.degree(G).values(),reverse=True) # degree sequence
print "Degree sequence", degree_sequence
dmax=max(degree_sequence)

plt.hist(degree_sequence,bins=dmax)
plt.title("Degree histogram")
plt.ylabel("count")
plt.xlabel("degree")

# draw graph in inset 
plt.axes([0.45,0.45,0.45,0.45])
Gcc=nx.connected_component_subgraphs(G)[0]
pos=nx.spring_layout(Gcc)
plt.axis('off')
nx.draw_networkx_nodes(Gcc,pos,node_size=20)
nx.draw_networkx_edges(Gcc,pos,alpha=0.4)

plt.savefig("degree_histogram.png")
plt.show()