Introduction to the Modeling and Analysis of Complex Systems

16.3. SIMULATING DYNAMICS OF NETWORKS 351Let’s simulate this model using Python. When you simulate the dynamics of networks,one practical challenge is how to visualize topological changes of the network. Unlikenode states that can be easily visualized using colors, network topology is the shape ofthe network itself, and if the shape of the network is changing dynamically, we also needto simulate the physical movement of nodes in the visualization space as well. This is justfor aesthetic visualization only, which has nothing to do with the real science going on inthe network. But an effective visualization often helps us better understand what is goingon in the simulation, so let’s try some fancy animation here. Fortunately, NetworkX’sspring_layout function can be used to update the current node positions slightly. Forexample:Code 16.9:g.pos = nx.spring_layout(g, pos = g.pos, iterations = 5)This code calculates a new set of node positions by using g.pos as the initial positionsand by applying the Fruchterman-Reingold force-directed algorithm to them for just fivesteps. This will effectively simulate a slight movement of the nodes from their currentpositions, which can be utilized to animate the topological changes smoothly.Here is an example of the completed simulation code for the small-world network formationby random edge rewiring:Code 16.10: small-world.pyimport matplotlibmatplotlib.use(’TkAgg’)from pylab import *import networkx as nximport random as rdn = 30 # number of nodesk = 4 # number of neighbors of each nodedef initialize():global gg = nx.Graph()for i in xrange(n):for j in range(1, k/2 + 1):g.add_edge(i, (i + j) % n)g.add_edge(i, (i - j) % n)