Introduction to the Modeling and Analysis of Complex Systems

396CHAPTER 17. DYNAMICAL NETWORKS II: ANALYSIS OF NETWORK TOPOLOGIES202log F(k)468101.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0log kFigure 17.11: Visual output of Code 17.17.According to this result, the CCDF had a negative exponent of about -1.97. Since thisvalue corresponds to −(γ − 1), the actual scaling exponent γ is about 2.97, which is prettyclose to its theoretical value, 3.Exercise 17.12 Obtain a large network data set whose degree distribution appearsto follow a power law, from any source (there are tons available online, includingMark Newman’s that was introduced before). Then estimate its scalingexponent using linear regression.17.6 AssortativityDegrees are a metric measured on individual nodes. But when we focus on the edges,there are always two degrees associated with each edge, one for the node where the edgeoriginates and the other for the node to where the edge points. So if we take the formerfor x and the latter for y from all the edges in the network, we can produce a scatter plotthat visualizes a possible degree correlation between the nodes across the edges. Suchcorrelations of node properties across edges can be generally described with the conceptof assortativity: