Introduction to the Modeling and Analysis of Complex Systems

16.2. SIMULATING DYNAMICS ON NETWORKS 339def update():global g, nextgfor i in g.nodes_iter():ci = g.node[i][’state’]nextg.node[i][’state’] = ci + alpha * ( \sum(g.node[j][’state’] for j in g.neighbors(i)) \- ci * g.degree(i)) * Dtg, nextg = nextg, gAnd then we can simulate a nice smooth diffusion process on a network, as shown inFig. 16.5, where continuous node states are represented by shades of gray. You can seethat the diffusion makes the entire network converge to a homogeneous configuration withthe average node state (around 0.5, or half gray) everywhere.Figure 16.5: Visual output of Code 16.7. Time flows from left to right.Exercise 16.6 This diffusion model conserves the sum of the node states. Confirmthis by revising the code to measure the sum of the node states during thesimulation.Exercise 16.7 Simulate a diffusion process on each of the following networktopologies, and then discuss how the network topology affects the diffusion onit. For example, does it make diffusion faster or slower?• random graph