Introduction to the Modeling and Analysis of Complex Systems

388CHAPTER 17. DYNAMICAL NETWORKS II: ANALYSIS OF NETWORK TOPOLOGIESfrom pylab import *import networkx as nxpdata = []Ldata = []Cdata = []g0 = nx.watts_strogatz_graph(1000, 10, 0)L0 = nx.average_shortest_path_length(g0)C0 = nx.average_clustering(g0)p = 0.0001while p < 1.0:g = nx.watts_strogatz_graph(1000, 10, p)pdata.append(p)Ldata.append(nx.average_shortest_path_length(g) / L0)Cdata.append(nx.average_clustering(g) / C0)p *= 1.5semilogx(pdata, Ldata, label = ’L / L0’)semilogx(pdata, Cdata, label = ’C / C0’)xlabel(’p’)legend()show()The result is shown in Fig. 17.7, where the characteristic path length (L) and the averageclustering coefficient (C) are plotted as their fractions to the baseline values (L0, C0)obtained from a purely regular network g0. As you can see in the figure, the networkbecomes very small (low L) yet remains highly clustered (high C) at the intermediate valueof p around 10 −2 . This is the parameter regime where the Watts-Strogatz small-worldnetworks arise.Exercise 17.10 Revise Code 17.12 so that you generate multiple Watts-Strogatznetworks for each p and calculate the averages of characteristic path lengths andaverage clustering coefficients. Then run the revised code to obtain a smoothercurve.