Introduction to the Modeling and Analysis of Complex Systems

17.5. DEGREE DISTRIBUTION 395logkdata = []logFdata = []prevF = ccdf[0]for k in domain:F = ccdf[k]if F != prevF:logkdata.append(log(k))logFdata.append(log(F))prevF = Fa, b, r, p, err = st.linregress(logkdata, logFdata)print ’Estimated CCDF: F(k) =’, exp(b), ’* k^’, aprint ’r =’, rprint ’p-value =’, pplot(logkdata, logFdata, ’o’)kmin, kmax = xlim()plot([kmin, kmax],[a * kmin + b, a * kmax + b])xlabel(’log k’)ylabel(’log F(k)’)show()In the second code block, the domain and ccdf were converted to log scales for linearfitting. Also, note that the original ccdf contained values for all k’s, even for those forwhich P (k) = 0. This would cause unnecessary biases in the linear regression toward thehigher k end where actual samples were very sparse. To avoid this, only the data pointswhere the value of F changed (i.e., where there were actual nodes with degree k) arecollected in the logkdata and logFdata lists.The result is shown in Fig. 17.11, and also the following output comes out to theterminal, which indicates that this was a pretty good fit:Code 17.18:Estimated CCDF: F(k) = 27.7963518947 * k^ -1.97465957944r = -0.997324657337p-value = 8.16476416778e-127