Introduction to the Modeling and Analysis of Complex Systems

368 CHAPTER 16. DYNAMICAL NETWORKS I: MODELINGdef 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’] - ci) * g.edge[i][j][’weight’]for j in g.neighbors(i))) * Dtfor i, j in g.edges_iter():wij = g.edge[i][j][’weight’]nextg.edge[i][j][’weight’] = wij + beta * wij * (1 - wij) * ( \1 - gamma * abs(g.node[i][’state’] - g.node[j][’state’])) * Dtnextg.pos = nx.spring_layout(nextg, pos = g.pos, iterations = 5)g, nextg = nextg, gimport pycxsimulatorpycxsimulator.GUI().start(func=[initialize, observe, update])In the initialize function, the edge weights are all initialized as 0.5, while node statesare set to 1 if the node belongs to Mr. Hi’s faction, or 0 otherwise. There are alsosome modifications made to the observe function. Since the edges carry weights, weshould color each edge in a different gray level. Therefore additional options (edge_color,edge_cmap, edge_vmin, and edge_vmax) were used to draw the edges in different colors.The update function is pretty straightforward, I hope.Figure 16.14 shows the simulation result with α = 1, β = 3, γ = 3. With this setting,unfortunately, the edge weights became weaker and weaker between the two politicalfactions (while they became stronger within each), and the Karate Club was eventuallysplit into two, which was what actually happened. In the meantime, we can also seethat there were some cultural/ideological diffusion taking place across the two factions,because their colors became a little more gray-ish than at the beginning. So, there wasapparently a competition not just between the two factions, but also between the twodifferent dynamics: social assimilation and fragmentation. History has shown that thefragmentation won in the actual Karate Club case, but we can explore the parameterspace of this model to see if there was any alternative future possible for the Karate Club!Exercise 16.21 Examine, by simulations, the sensitivity of the Karate Club adaptivediffusion model on the initial node state assignments. Can a different node