Socioeconomic Networks with Long-Range Interactions

TL;DR

This paper explores how socioeconomic networks evolve with long-range interactions, showing that the structure shifts from power-law to exponential degree distributions as the influence of distance varies, affecting network utility and topology.

Contribution

Introduces a modified socioeconomic network model with a growth mechanism based on utility, analyzing how network structure changes with distance decay parameter and comparing utilities across network types.

Findings

Network structure shifts from power-law to exponential with increasing $oldsymbol{\delta}$.

Power-law networks yield higher average utility than Poisson networks.

Network properties like path length and assortativity vary with $oldsymbol{\delta}$.

Abstract

We study a modified version of a model previously proposed by Jackson and Wolinsky to account for communicating information and allocating goods in socioeconomic networks. In the model, the utility function of each node is given by a weighted sum of contributions from all accessible nodes. The weights, parameterized by the variable $\delta$, decrease with distance. We introduce a growth mechanism where new nodes attach to the existing network preferentially by utility. By increasing $\delta$, the network structure evolves from a power-law to an exponential degree distribution, passing through a regime characterised by shorter average path length, lower degree assortativity and higher central point dominance. In the second part of the paper we compare different network structures in terms of the average utility received by each node. We show that power-law networks provide higher average utility than Poisson random networks. This provides a possible justification for the ubiquitousness of scale-free networks in the real world.