Generate modified small-world networks and compare with theoretical predictions.
Generate and analyze small-world networks according to the revised Watts-Strogatz model where the randomization at β = 1 is truly equal to the Erdős-Rényi network model.
In the Watts-Strogatz model each node rewires its k/2 rightmost edges with probality β. This means that each node has halways minimum degree k/2. Also, at β = 1, each edge has been rewired. Hence the probability of it existing is smaller than k/(N-1), contrary to the ER model.
In the adjusted model, each pair of nodes is connected with a certain connection probability. If the lattice distance between the potentially connected nodes is d(i,j) <= k/2 then they are connected with short-range probability p_S = k / (k + β (N-1-k)), otherwise they’re connected with long-range probability p_L = β * p_S.
pip install smallworld
Beware: smallworld only works with Python 3!
In the following example you can see how to generate and draw according to the model described above.
from smallworld.draw import draw_network from smallworld import get_smallworld_graph import matplotlib.pyplot as pl # define network parameters N = 21 k_over_2 = 2 betas = [0, 0.025, 1.0] labels = [ r'$\beta=0$', r'$\beta=0.025$', r'$\beta=1$'] focal_node = 0 fig, ax = pl.subplots(1,3,figsize=(9,3)) # scan beta values for ib, beta in enumerate(betas): # generate small-world graphs and draw G = get_smallworld_graph(N, k_over_2, beta) draw_network(G,k_over_2,focal_node=focal_node,ax=ax[ib]) ax[ib].set_title(labels[ib],fontsize=11) # show pl.subplots_adjust(wspace=0.3) pl.show()
Download the file for your platform. If you're not sure which to choose, learn more about installing packages.
|Filename, size||File type||Python version||Upload date||Hashes|
|Filename, size smallworld-0.0.2.tar.gz (7.6 kB)||File type Source||Python version None||Upload date||Hashes View hashes|