A Stochastic Evolutionary Model Exhibiting Power-Law Behaviour with an Exponential Cutoff

TL;DR

This paper introduces a modified stochastic evolutionary model for complex networks that naturally produces power-law distributions with exponential cutoffs, aligning better with real-world network data such as protein interactions.

Contribution

The authors propose a new model incorporating node removal probability, capturing power-law with exponential cutoff distributions, especially for exponents less than or equal to two.

Findings

Model produces power-law with exponential cutoff distributions.

Analysis of yeast protein network confirms model's applicability.

Captures phenomena in limited-size networks like protein and email networks.

Abstract

Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get richer'' phenomenon. Despite the generality of the proposed stochastic models, there are still some unexplained phenomena, which may arise due to the limited size of networks such as protein and e-mail networks. Such networks may in fact exhibit an exponential cutoff in the power-law scaling, although this cutoff may only be observable in the tail of the distribution for extremely large networks. We propose a modification of the basic stochastic evolutionary model, so that after a node is chosen preferentially, say according to the number of its inlinks, there is a small probability that this node will be discarded. We show that as a result of this modification, by viewing the stochastic process in terms of an urn transfer model, we obtain a power-law distribution with an exponential cutoff. Unlike many other models, the current model can capture instances where the exponent of the distribution is less than or equal to two. As a proof of concept, we demonstrate the consistency of our model by analysing a yeast protein interaction network, the distribution of which is known to follow a power law with an exponential cutoff.