Carrying capacity in growing networks

TL;DR

This paper introduces a growing network model with finite degree over infinite time, analyzing its degree distribution and hub formation through exact results and simulations, revealing scaling behavior and competitive linking dynamics.

Contribution

It presents a novel growing network model governed by Malthus-Verhulst-like dynamics, with analytical and simulation-based analysis of degree distribution and hub accumulation.

Findings

Degree distribution exhibits scaling at large times

Finite-time dynamics show hub accumulation due to competing linking factors

Model achieves finite degrees in infinite time, unlike traditional models

Abstract

In this work, a growing network model that can generate a random network with finite degree in infinite time is studied. The dynamics are governed by a rule where the degree increases under a scheme similar to the Malthus-Verhulst model in the context of population growth. The degree distribution is analysed in both stationary and time-dependent regimes through some exact results and simulations, and a scaling behaviour is found in asymptotically large time. For finite times, the time-dependent degree distribution displays an accumulation of hubs as a result of competition between attractive and repulsive terms in linking probability.