An Information Theory Approach to Network Evolution Models

TL;DR

This paper introduces a new Markovian network evolution model using information theory, analyzing its properties, entropy, and simulation methods, including a subset matching the Erdos-Renyi model.

Contribution

The paper presents the Network Evolution Chain, a novel Markovian model with proven stationarity, ergodicity, and entropy characteristics, along with a specialized Erdos-Renyi subset.

Findings

The model is stationary and ergodic.

Entropy rate and typical sequences are characterized.

Simulation results support theoretical findings.

Abstract

A novel Markovian network evolution model is introduced and analysed by means of information theory. It will be proved that the model, called Network Evolution Chain, is a stationary and ergodic stochastic process. Therefore, the Asymptotic Equipartition Property can be applied to it. The model's entropy rate and typical sequences are also explored. Extracting particular information from the network and methods to simulate network evolution in the continuous time domain are discussed. Additionally, the Erdos-Renyi Network Evolution Chain is introduced as a subset of our model with the additional property of its stationary distribution matching the Erdos-Renyi random graph model. The stationary distributions of nodes and graphs are calculated for this subset alongside its entropy rate. The simulation results at the end of the paper back up the proved theorems and calculated values.