Introduction to the Modeling and Analysis of Complex Systems

326 CHAPTER 16. DYNAMICAL NETWORKS I: MODELINGdynamically change adaptively to each other. Adaptive network models try to unify differentdynamical network models to provide a generalized modeling framework for complexsystems, since many real-world systems show such adaptive network behaviors [67].16.2 Simulating Dynamics on NetworksBecause NetworkX adopts plain dictionaries as their main data structure, we can easilyadd states to nodes (and edges) and dynamically update those states iteratively. This isa simulation of dynamics on networks. This class of dynamical network models describesdynamic state changes taking place on a static network topology. Many real-world dynamicalnetworks fall into this category, including:• Regulatory relationships among genes and proteins within a cell, where nodes aregenes and/or proteins and the node states are their expression levels.• Ecological interactions among species in an ecosystem, where nodes are speciesand the node states are their populations.• Disease infection on social networks, where nodes are individuals and the nodestates are their epidemiological states (e.g., susceptible, infected, recovered, immunized,etc.).• Information/culture propagation on organizational/social networks, where nodes areindividuals or communities and the node states are their informational/cultural states.The implementation of simulation models for dynamics on networks is strikingly similarto that of CA. You may find it even easier on networks, because of the straightforwarddefinition of “neighbors” on networks. Here, we will work on a simple local majority ruleon a social network, with the following assumptions:• Nodes represent individuals, and edges represent their symmetric connections forinformation sharing.• Each individual takes either 0 or 1 as his or her state.• Each individual changes his or her state to a majority choice within his or her localneighborhood (i.e., the individual him- or herself and the neighbors connected tohim or her). This neighborhood is also called the ego network of the focal individualin social sciences.