Weighted Scale-free Networks in Euclidean Space Using Local Selection Rule

TL;DR

This paper introduces a spatial scale-free network model based on local connection rules inspired by real-world networks like the Internet and airports, analyzing its properties and comparing it to the BA model.

Contribution

The study presents a novel spatial scale-free network model using local selection rules, with analytical results on link weights and node strength, differing from traditional preferential attachment models.

Findings

Network exhibits BA-like degree distribution despite local connection rule.

Link weights follow a power-law decay over time.

Node strength depends non-linearly on degree.

Abstract

A spatial scale-free network is introduced and studied whose motivation has been originated in the growing Internet as well as the Airport networks. We argue that in these real-world networks a new node necessarily selects one of its neighbouring local nodes for connection and is not controlled by the preferential attachment as in the Barab\'asi-Albert (BA) model. This observation has been mimicked in our model where the nodes pop-up at randomly located positions in the Euclidean space and are connected to one end of the nearest link. In spite of this crucial difference it is observed that the leading behaviour of our network is like the BA model. Defining link weight as an algebraic power of its Euclidean length, the weight distribution and the non-linear dependence of the nodal strength on the degree are analytically calculated. It is claimed that a power law decay of the link weights with time ensures such a non-linear behavior. Switching off the Euclidean space from the same model yields a much simpler definition of the Barab\'asi-Albert model where numerical effort grows linearly with $N$.