Introduction to the Modeling and Analysis of Complex Systems

16.3. SIMULATING DYNAMICS OF NETWORKS 359Exercise 16.15 Simulate the Barabási-Albert network growth model with m = 1,m = 3, and m = 5, and see how the growth process may be affected by thevariation of this parameter.Exercise 16.16 Modify the preferential node selection function so that the nodeselection probability p(i) is each of the following:• independent of the node degree (random attachment)• proportional to the square of the node degree (strong preferential attachment)• inversely proportional to the node degree (negative preferential attachment)Conduct simulations for these cases and compare the resulting network topologies.Note that NetworkX has a built-in graph generator function for the Barabási-Albertscale-free networks too, called barabasi_albert_graph(n, m). Here, n is the number ofnodes, and m the number of edges by which each newcomer node is connected to thenetwork.Here are some more exercises of dynamics of networks models, for your further exploration:Exercise 16.17 Closing triangles This example is a somewhat reversed versionof the Watts-Strogatz small-world network model. Instead of making a local,clustered network to a global, unclustered network, we can consider a dynamicalprocess that makes an unclustered network more clustered over time. Here arethe rules:• The network is initially random, e.g., an Erdős-Rényi random graph.• In each iteration, a two-edge path (A-B-C) is randomly selected from the network.• If there is no edge between A and C, one of them loses one of its edges (butnot the one that connects to B), and A and C are connected to each otherinstead.This is an edge rewiring process that closes a triangle among A, B, and C, promotingwhat is called a triadic closure in sociology. Implement this edge rewiringmodel, conduct simulations, and see what kind of network topology results from