networks with random power-law distributed weights

Question

How can I randomly assign weights from a power-law distribution to a network with very large number of nodes.

I wrote

import networkx as nx
import numpy as np
from networkx.utils import powerlaw_sequence

z=nx.utils.create_degree_sequence(200,nx.utils.powerlaw_sequence,exponent=1.9)
nx.is_valid_degree_sequence(z) 
G=nx.configuration_model(z)
Gcc=nx.connected_component_subgraphs(G)[0]

edgelist=[nx.utils.powerlaw_sequence(nx.number_of_edges(Gcc),exponent=2.0)]

I know I assign weights to edges by a dictionary of tuples (node1,node2,weight) using:

nx.from_edgelist(edgelist,create_using=None)

But when I am just interested in getting a weighted network where weights are power-law distributed, is there another shorter way?

Answer 1

You can assign weights directly using G[u][v]['weight'], for example

In [1]: import networkx as nx

In [2]: import random

In [3]: G = nx.path_graph(10)

In [4]: for u,v in G.edges():
   ...:     G[u][v]['weight'] = random.paretovariate(2)
   ...:     
   ...:     

In [5]: print G.edges(data=True)
[(0, 1, {'weight': 1.6988521989583232}), (1, 2, {'weight': 1.0749963615177736}), (2, 3, {'weight': 1.1503859779558812}), (3, 4, {'weight': 1.675436575683888}), (4, 5, {'weight': 1.1948608572552846}), (5, 6, {'weight': 1.080152340891444}), (6, 7, {'weight': 1.0296667672332183}), (7, 8, {'weight': 2.0014384064255446}), (8, 9, {'weight': 2.2691612212058447})]

I used Python's random.paretovariate() to choose the weight but you can, of course, put whatever you want there.

Answer 2

I tried and got the following.. I hope it helps. Also, I am looking for better methods as this does not insure I get a connected network. Also, I have still to check its properties.

'''written by Aya Al-Zarka'''

import networkx as nx
import matplotlib.pyplot as plt
from networkx.utils import powerlaw_sequence
import random as r
import numpy as np

G=nx.Graph()
v=[]
for i in range(100):
v.append(i)

G.add_nodes_from(v)

weight=[]
for j in range(300):
   l=powerlaw_sequence(300,exponent=2.0)
   weight.append(r.choice(l))
#print(weight)
e=[]
for k in range(300):
   f=[r.choice(v),r.choice(v),r.choice(weight)]
   e.append(f)

G.add_weighted_edges_from(e,weight='weight')

print(nx.is_connected(G)) #not always!


m=np.divide(weight,100.0)
pos=nx.random_layout(G,dim=2)
nx.draw_networkx_nodes(G,pos,nodelist=None,node_size=300,node_color='y',
                   node_shape='*', alpha=1.0, cmap=None, vmin=None,
                   vmax=None, ax=None, linewidths=None,)
 nx.draw_networkx_edges(G,pos,edgelist=None,width=m,
edge_color='b',style='solid',alpha=None,edge_cmap=None, edge_vmin=None,
edge_vmax=None, ax=None, arrows=False)
plt.ylim(0,1)
plt.xlim(0,1)
plt.axis('off')
plt.show()