Network growth with preferential attachment and without "rich get richer" mechanism

TL;DR

This paper introduces a new network growth model based on preferential attachment that favors less connected nodes, resulting in an exponential degree distribution, contrasting with the power-law distribution of traditional models.

Contribution

It presents a novel preferential attachment model that excludes the 'rich get richer' mechanism, providing insights into how degree distributions emerge without it.

Findings

The model produces exponential degree distributions.

Numerical results align with the master equation solution.

Comparison shows differences from the BA model's power-law distribution.

Abstract

We propose a simple preferential attachment model of growing network using the complementary probability of Barab\'asi-Albert (BA) model, i.e., $\Pi(k_i) \propto 1-\frac{k_i}{\sum_j k_j}$. In this network, new nodes are preferentially attached to not well connected nodes. Numerical simulations, in perfect agreement with the master equation solution, give an exponential degree distribution. This suggests that the power law degree distribution is a consequence of preferential attachment probability together with "rich get richer" phenomena. We also calculate the average degree of a target node at time t $(<k_s(t)>)$ and its fluctuations, to have a better view of the microscopic evolution of the network, and we also compare the results with BA model.