Effect of congestion costs on shortest paths through complex networks

TL;DR

This paper analytically examines how congestion costs influence shortest path routing in complex networks, revealing an optimal hub connectivity that balances centralized and decentralized transport for improved efficiency.

Contribution

It introduces a solvable network model incorporating congestion costs, demonstrating the existence of an optimal number of hub connections to minimize shortest paths.

Findings

Optimal number of hub connections exists for minimal shortest path

Congestion costs create a trade-off between centralized and decentralized routing

Results applicable to biological, informational, and social networks

Abstract

We analyze analytically the effect of congestion costs within a physically relevant, yet exactly solvable network model featuring central hubs. These costs lead to a competition between centralized and decentralized transport pathways. In stark contrast to conventional no-cost networks, there now exists an optimal number of connections to the central hub in order to minimize the shortest path. Our results shed light on an open problem in biology, informatics and sociology, concerning the extent to which decentralized versus centralized design benefits real-world complex networks.