Effect of diffusion of elements on network topology and self-organization

TL;DR

This paper investigates how the diffusion of elements affects network topology and self-organization, revealing deviations from pure scale-free behavior and highlighting the influence of local memory and interactions during network growth.

Contribution

It introduces a model incorporating element diffusion and local memory effects, demonstrating their impact on network degree distribution and stability, with numerical evidence supporting approximate scale-free properties.

Findings

Degree distribution deviates from pure scale-free, showing exponential decay.

Local memory influences network stability and topological reorganization.

Network approximately retains scale-free properties despite deviations.

Abstract

We study the influence of elements diffusing in and out of a network to the topological changes of the network and characterize it by investigating the behavior of probability of degree distribution ($\Gamma(k)$) with degree $k$. The local memory of the incoming element and its interaction with the elements already present in the network during the growing process significantly affect the network stability which in turn reorganize the network properties. We found that the properties of $\Gamma(k)$ of this network are deviated from scale free type, where the power law behavior contains a exponentially decay factor supporting earlier reported results of Amaral et.al. \cite{ama} and Newman \cite{new1} and recent statistical analysis results on degree distribution data of some scale free network [11]. Our numerical results also support the behavior of this $\Gamma(k)$. However, we found numerically the contribution from exponential factor to the $\Gamma(k)$ to be very weak as compared to the scale free factor showing that the network as a whole carries the scale free properties approximately.