Effect of node attributes on the temporal dynamics of network structure

Many natural and social networks evolve in time and their structures are dynamic. In most networks, nodes are heterogeneous, and their roles in the evolution of structure differ. This paper focuses on the role of individual attributes on the temporal dynamics of network structure. We focus on a basic model for growing networks that incorporates node attributes (which we call "quality"), and we focus on the problem of forecasting the structural properties of the network in arbitrary times for an arbitrary initial network. That is, we address the following question: If we are given a certain initial network with given arbitrary structure and known node attributes, then how does the structure change in time as new nodes with given distribution of attributes join the network? We solve the model analytically and obtain the quality-degree joint distribution and degree correlations. We characterize the role of individual attributes in the position of individual nodes in the hierarchy of connections. We confirm the theoretical findings with Monte Carlo simulations.