Introduction to the Modeling and Analysis of Complex Systems

16.3. SIMULATING DYNAMICS OF NETWORKS 353function.Running this code will give you an animated process of random edge rewiring, whichgradually turns a regular, local, clustered network to a random, global, unclustered one(Fig. 16.9). Somewhere in this network dynamics, you will see the Watts-Strogatz smallworldnetwork arise, but just temporarily (which will be discussed further in the next chapter).Figure 16.9: Visual output of Code 16.10. Time flows from left to right.Exercise 16.14 Revise the small-world network formation model above so thatthe network is initially a two-dimensional grid in which each node is connected to itsfour neighbors (north, south, east, and west; except for those on the boundaries ofthe space). Then run the simulations, and see how random edge rewiring changesthe topology of the network.For your information, NetworkX already has a built-in graph generator function forWatts-Strogatz small-world networks, watts_strogatz_graph(n, k, p). Here, n is thenumber of nodes, k is the degree of each node, and p is the edge rewiring probability. Ifyou don’t need to simulate the formation of small-world networks iteratively, you shouldjust use this function instead.Scale-free networks by preferential attachment The Watts-Strogatz small-world networkmodel brought about a major breakthrough in explaining properties of real-worldnetworks using abstract network models. But of course, it was not free from limitations.First, their model required a “Goldilocks” rewiring probability p (or such a simulation lengthin our revised model) in order to obtain a small-world network. This means that their model