Fitness-driven deactivation in network evolution

TL;DR

This paper introduces a model of network evolution driven by intrinsic node fitness and aging, explaining how networks grow and decay with different structures and universal clustering laws.

Contribution

It presents a new fitness-based aging mechanism for network evolution, deriving structured exponential and scale-free networks with universal clustering laws.

Findings

Homogeneous fitness leads to exponential networks.

Heterogeneous fitness results in scale-free networks.

Universal clustering laws $C(k) o k^{-1}$ and $C o n^{-1}$ are established.

Abstract

Individual nodes in evolving real-world networks typically experience growth and decay --- that is, the popularity and influence of individuals peaks and then fades. In this paper, we study this phenomenon via an intrinsic nodal fitness function and an intuitive aging mechanism. Each node of the network is endowed with a fitness which represents its activity. All the nodes have two discrete stages: active and inactive. The evolution of the network combines the addition of new active nodes randomly connected to existing active ones and the deactivation of old active nodes with possibility inversely proportional to their fitnesses. We obtain a structured exponential network when the fitness distribution of the individuals is homogeneous and a structured scale-free network with heterogeneous fitness distributions. Furthermore, we recover two universal scaling laws of the clustering coefficient for both cases, $C(k) \sim k^{-1}$ and $C \sim n^{-1}$, where $k$ and $n$ refer to the node degree and the number of active individuals, respectively. These results offer a new simple description of the growth and aging of networks where intrinsic features of individual nodes drive their popularity, and hence degree.