Introduction to the Modeling and Analysis of Complex Systems

360 CHAPTER 16. DYNAMICAL NETWORKS I: MODELINGthis triadic closure rule. You can also combine this rule with the random edgerewiring used in the Watts-Strogatz model, to explore various balances betweenthese two competing rules (globalization and localization) that shape the selforganizationof the network topology.Exercise 16.18 Preferential attachment with node division We can considera modification of the Barabási-Albert model where each node has a capacity limitin terms of the number of connections it can hold. Assume that if a node’s degreeexceeds its predefined capacity, the node splits into two, and each node inheritsabout half of the connections the original node had. This kind of node divisioncan be considered a representation of a split-up of a company or an organization,or the evolution of different specialized genes from a single gene that had manyfunctions. Implement this modified network growth model, conduct simulations,and see how the node division influences the resulting network topology.16.4 Simulating Adaptive NetworksThe final class of dynamical network models is that of adaptive networks. It is a hybrid ofdynamics on and of networks, where states and topologies “co-evolve,” i.e., they interactwith each other and keep changing, often over the same time scales. The word “adaptive”comes from the concept that states and topologies can adapt to each other in a coevolutionarymanner, although adaptation or co-evolution doesn’t have to be biological inthis context. Adaptive networks have been much less explored compared to the othertwo classes of models discussed above, but you can find many real-world examples ofadaptive networks [67], such as:• Development of an organism. The nodes are the cells and the edges are cellcelladhesions and intercellular communications. The node states include intracellulargene regulatory and metabolic activities, which are coupled with topologicalchanges caused by cell division, death, and migration.• Self-organization of ecological communities. The nodes are the species and theedges are the ecological relationships (predation, symbiosis, etc.) among them. Thenode states include population levels and within-species genetic diversities, whichare coupled with topological changes caused by invasion, extinction, adaptation,and speciation.