Introduction to the Modeling and Analysis of Complex Systems

16.4. SIMULATING ADAPTIVE NETWORKS 365Adaptive diffusion model The final example in this chapter is the adaptive network versionof the continuous state/time diffusion model, where the weight of a social tie can bestrengthened or weakened according to the difference of the node states across the edge.This new assumption represents a simplified form of homophily, an empirically observedsociological fact that people tend to connect those who are similar to themselves. In contrast,the diffusion of node states can be considered a model of social contagion, anotherempirically observed sociological fact that people tend to become more similar to theirsocial neighbors over time. There has been a lot of debate going on about which mechanism,homophily or social contagion, is more dominant in shaping the structure of socialnetworks. This adaptive diffusion model attempts to combine these two mechanisms toinvestigate their subtle balance via computer simulations.This example is actually inspired by an adaptive network model of a corporate mergerthat my collaborator Junichi Yamanoi and I presented recently [73]. We studied the conditionsfor two firms that recently underwent a merger to successfully assimilate and integratetheir corporate cultures into a single, unified identity. The original model was abit complex agent-based model that involved asymmetric edges, multi-dimensional statespace, and stochastic decision making, so here we use a more simplified, deterministic,differential equation-based version. Here are the model assumptions:• The network is initially made of two groups of nodes with two distinct cultural/ideologicalstates.• Each edge is undirected and has a weight, w ∈ [0, 1], which represents the strengthof the connection. Weights are initially set to 0.5 for all the edges.• The diffusion of the node states occurs according to the following equation:dc idt = α ∑ j∈N i(c j − c i )w ij (16.18)Here α is the diffusion constant and w ij is the weight of the edge between node iand node j. The inclusion of w ij signifies that diffusion takes place faster throughedges with greater weights.• In the meantime, each edge also changes its weight dynamically, according to thefollowing equation:dw ijdt= βw ij (1 − w ij )(1 − γ |c i − c j | ) (16.19)