Efficient Network Structures with Separable Heterogeneous Connection Costs

TL;DR

This paper introduces a model for network formation with separable, degree-proportional costs, revealing that efficient networks tend to have a core-periphery structure and providing bounds on clustering.

Contribution

It presents an analytical solution for efficient networks under heterogeneous, separable costs and explores their stability and structural properties.

Findings

Efficient networks have a core-periphery structure.

A lower bound for clustering coefficient is derived.

Separable costs influence network stability and structure.

Abstract

We introduce a heterogeneous connection model for network formation to capture the effect of cost heterogeneity on the structure of efficient networks. In the proposed model, connection costs are assumed to be separable, which means the total connection cost for each agent is uniquely proportional to its degree. For these sets of networks, we provide the analytical solution for the efficient network and discuss stability impli- cations. We show that the efficient network exhibits a core-periphery structure, and for a given density, we find a lower bound for clustering coefficient of the efficient network.