Visibility of Nodes in Network Growth Models

Many real-world complex networks can be synthesized using growth models, where nodes enter the network at discrete time steps and attach with existing nodes based on their degree, or fitness, or a combination of both. While, the literature has mostly focused on the asymptotic global properties of such models, e.g., degree distribution, we intend to drive the focus towards investigating the dynamics from the perspective of individual nodes. In this paper, we study how the visibility of a node, i.e., the probability of the node to form new connections, changes over time. In particular, we study three well-known network growth models—preferential attachment, additive and multiplicative fitness models, and focus primarily on “influential nodes” or “leaders” to understand how their visibility changes over time. We present a thorough analytical study and validate our claims through simulations. Our primary finding is that influential nodes in multiplicative growth models can attain and maintain high visibility over time compared to other models; something that might not be apparent by simply looking at global network properties or other local node-centric properties.