Abstract by Erik Hannesson
Network Synchronization, Structure, and Specialization
Network theory seeks to understand both the dynamics of networks and the dynamics on networks; that is, the evolution of network topology and the evolution of network states, respectively. Both topics prove complicated in their own right and are typically not considered together. Here we consider a model for network growth, called specialization, that allows us to simultaneously analyze dynamics of and dynamics on networks.
Specifically, we explore the interplay between how changing network topology alters the dynamics on the network and, in turn, how the dynamics on the network can influence change in topology. We introduce theoretical results that provide conditions guaranteeing community synchronization in specialized networks. Furthermore, we introduce closely related statistical results describing real-world networks, random networks, and specialized networks in terms of equitable partitions.