Detecting differences in the topology of scale-free networks grown under time-dynamic topological fitness

Dimitrios Tsiotas

doi:10.1038/s41598-020-67156-6

Abstract

The fitness model was introduced in the literature to expand the Barabasi-Albert model’s generative mechanism, which produces scale-free networks under the control of degree. However, the fitness model has not yet been studied in a comprehensive context because most models are built on invariant fitness as the network grows and time-dynamics mainly concern new nodes joining the network. This mainly static consideration restricts fitness in generating scale-free networks only when the underlying fitness distribution is power-law, a fact which makes the hybrid fitness models based on degree-driven preferential attachment to remain the most attractive models in the literature. This paper advances the time-dynamic conceptualization of fitness, by studying scale-free networks generated under topological fitness that changes as the network grows, where the fitness is controlled by degree, clustering coefficient, betweenness, closeness, and eigenvector centrality. The analysis shows that growth under time-dynamic topological fitness is indifferent to the underlying fitness distribution and that different topological fitness generates networks of different topological attributes, ranging from a mesh-like to a superstar-like pattern. The results also show that networks grown under the control of betweenness centrality outperform the other networks in scale-freeness and the majority of the other topological attributes. Overall, this paper contributes to broadening the conceptualization of fitness to a more time-dynamic context.

Highlights

The fitness model was introduced in the literature to expand the Barabasi-Albert model’s generative mechanism, which produces scale-free networks under the control of degree
The statistical inference analysis illustrates that many topological aspects differ amongst the available null-model families. This implies that networks generated under time-dynamic topological fitness considerably differ in their topological attributes
Aiming to broaden the time-dynamic conceptualization of fitness, this paper studied scale-free networks generated under time-dynamic topological fitness that changes as the network grows

Summary

Introduction

The fitness model was introduced in the literature to expand the Barabasi-Albert model’s generative mechanism, which produces scale-free networks under the control of degree. When node fitness is exclusively driven by node degree (φi = 1), the model is converted to the classic BA model shown in relation (1) Going beyond this consideration, the authors of[17] argued that the underlying fitness distributions (instead of by default the degree) are directly responsible for the emergence of scale-free networks. The authors of[17] argued that the underlying fitness distributions (instead of by default the degree) are directly responsible for the emergence of scale-free networks Within this free-of-degree context, they defined the connecting probability between a new (j) and an existing (i) node proportionally to the intrinsic (non-negative) fitness φi[13,17], according to the relation:.

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