Introduction to the Modeling and Analysis of Complex Systems

398CHAPTER 17. DYNAMICAL NETWORKS II: ANALYSIS OF NETWORK TOPOLOGIESxdata.append(ba.degree(j)); ydata.append(ba.degree(i))plot(xdata, ydata, ’o’, alpha = 0.05)show()In this example, we draw a degree-degree scatter plot for a Barabási-Albert network with1,000 nodes. For each edge, the degrees of its two ends are stored in xdata and ydatatwice in different orders, because an undirected edge can be counted in two directions.The markers in the plot are made transparent using the alpha option so that we can seethe density variations in the plot.The result is shown in Fig. 17.12, where each dot represents one directed edge in thenetwork (so, an undirected edge is represented by two dots symmetrically placed acrossa diagonal mirror line). It can be seen that most edges connect low-degree nodes to eachother, with some edges connecting low-degree and high-degree nodes, but it is quite rarethat high-degree nodes are connected to each other. Therefore, there is a mild negativedegree correlation in this case.Figure 17.12: Visual output of Code 17.19.We can confirm this observation by calculating the degree assortativity coefficient asfollows:Code 17.20: