# Analytic solution for preferential attachment probabilities scheme

## TL;DR

This paper presents an explicit analytical solution for the preferential attachment probabilities scheme, modeling it as a sequence of dependent Bernoulli variables to better understand scale-free network formation.

## Contribution

It introduces a novel explicit expression for transition probabilities in the preferential attachment scheme, framing it as dependent Bernoulli variables.

## Key findings

- Explicit transition probability formula derived
- Modeling as dependent Bernoulli variables enhances understanding
- Applicable to scale-free network analysis

## Abstract

Preferential attachment probabilities scheme appear in the context of scale free random graphs [1],[2]. In this work we present preferential attachment probabilities scheme as a sequence of dependent Bernoulli random variables and we give an explicit expression of the transition probabilities.