Preferential attachment with information filtering - node degree probability distribution properties

TL;DR

This paper introduces a network growth model using a two-step preferential attachment process that does not require global network knowledge, revealing an exponential tail in the node degree distribution.

Contribution

The study presents a novel two-step preferential attachment model and provides both simulation and theoretical analysis of its degree distribution, which was not previously explored.

Findings

Degree distribution tail is exponential, proportional to exp(-k/m)

Simulation and theoretical results are in excellent agreement

Model operates without global network knowledge

Abstract

A network growth mechanism based on a two-step preferential rule is investigated as a model of network growth in which no global knowledge of the network is required. In the first filtering step a subset of fixed size $m$ of existing nodes is randomly chosen. In the second step the preferential rule of attachment is applied to the chosen subset. The characteristics of thus formed networks are explored using two approaches: computer simulations of network growth and a theoretical description based on a master equation. The results of the two approaches are in excellent agreement. Special emphasis is put on the investigation of the node degree probability distribution. It is found that the tail of the distribution has the exponential form given by $exp(-k/m)$. Implications of the node degree distribution with such tail characteristics are briefly discussed.