A population evolution model and its applications to random networks

TL;DR

This paper introduces a general population evolution model where individuals are characterized by scores, deriving asymptotic theorems and demonstrating that the score distribution is scale-free, with applications to random network clique weight distributions.

Contribution

It presents a new, general population evolution model and proves its scale-free score distribution, applying it to analyze clique weights in random networks.

Findings

Score distribution is scale-free.

Asymptotic theorems for fixed score counts.

Application to random graph clique weights.

Abstract

A general population evolution model is considered. Any individual of the population is characterized by its score. Certain general conditions are assumed concerning the number of the individuals and their scores. Asymptotic theorems are obtained for the number of individuals having some fixed score. It is proved that the score distribution is scale free. The result is applied to obtain the weight distributions of the cliques in a random graph evolution model.