Power law random networks

Question

How can I randomly assign weights from a power law distribution to a network with a 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 that I assign weights to edges using the tuple dictionary (node1, node2, weight) using:

 nx.from_edgelist(edgelist,create_using=None) 

But when I'm just interested in getting a weighted network where weights are distributed according to a power law, is there another shorter way?

Answer 1

You can directly assign weights 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 random.paretovariate () to select the weight, but of course you can place whatever you want.

Answer 2

I tried and got the following. Hope this helps. Also, I am looking for better methods, as this does not guarantee that I get a connected network. In addition, I still need 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()