Evolving Networks Created by Preferential Attachment and Decay

TL;DR

This paper introduces an extension to preferential attachment models that allows networks to evolve through edge addition and removal while preserving a power law degree distribution, better reflecting real-world network dynamics.

Contribution

It presents a novel method to extend preferential attachment models to include edge decay and addition, maintaining scale-free properties in evolving networks.

Findings

Extended models preserve power law degree distribution with edge dynamics.

Evolving networks retain scale-free structure despite edge addition and removal.

Method improves realism of synthetic network growth simulations.

Abstract

Growing synthetic networks that follow power law distributions of a node's degree often involves adding one node at a time. Each node is added to the network with a fixed amount of edges and those edges are frozen for all future time steps. Yet real world networks often continuously evolve with edges being added and removed while new nodes are added to the network. Many existing growth models based on preferential attachment do not account for this evolutionary capability and when you extend their growth methods to add and remove edges to existing nodes the node degree distribution quickly loses its scale-free structure. This paper will go over a method to extend well known preferential attachment growth models to allow for the evolution of edges within a network while still maintaining a power law node degree distribution.