Introduction to the Modeling and Analysis of Complex Systems

332 CHAPTER 16. DYNAMICAL NETWORKS I: MODELINGas a “speaker” or a “listener.” The probability actually depends on how popular a nodeis. Specifically, the original version tends to choose higher-degree nodes as a speakermore often, while the reversed version tends to choose higher-degree nodes as a listenermore often. This is because of the famous friendship paradox, a counter-intuitive factfirst reported by sociologist Scott Feld in the 1990s [68], which is that a randomly selectedneighbor of a randomly selected node tends to have a larger-than-average degree.Therefore, it is expected that the original version of the voter model would promote homogenizationof opinions as it gives more speaking time to the popular nodes, while thereversed version would give an equal chance of speech to everyone so the opinion homogenizationwould be much slower, and the edge-based version would be somewherein between. We can check these predictions by computer simulations.The good news is that the simulation code of the voter model is much simpler than thatof the majority rule network model, because of the asynchrony of state updating. We nolonger need to use two separate data structures; we can keep modifying just one Graphobject directly. Here is a sample code for the original “pull” version of the voter model,again on the Karate Club graph:Code 16.5: voter-model.pyimport matplotlibmatplotlib.use(’TkAgg’)from pylab import *import networkx as nximport random as rddef initialize():global gg = nx.karate_club_graph()g.pos = nx.spring_layout(g)for i in g.nodes_iter():g.node[i][’state’] = 1 if random() < .5 else 0def observe():global gcla()nx.draw(g, cmap = cm.binary, vmin = 0, vmax = 1,node_color = [g.node[i][’state’] for i in g.nodes_iter()],pos = g.pos)