Small Worlds in Space: Synchronization, Spatial and Relational Modularity

TL;DR

This paper explores how networks optimized for synchronization and wiring cost form small world structures with spatial and relational modularity, revealing different configurations based on wiring cost.

Contribution

It introduces a model of spatially embedded networks optimized for synchronization and wiring cost, identifying conditions leading to various small world modular structures.

Findings

Low wiring cost leads to two spatial groups with maximum distance.

High wiring cost results in multiple spatial groups connected in a ring.

Intermediate costs produce networks with both spatial and relational modularity.

Abstract

In this Letter we investigate networks that have been optimized to realize a trade-off between enhanced synchronization and cost of wire to connect the nodes in space. Analyzing the evolved arrangement of nodes in space and their corresponding network topology a class of small world networks characterized by spatial and network modularity is found. More precisely, for low cost of wire optimal configurations are characterized by a division of nodes into two spatial groups with maximum distance from each other, whereas network modularity is low. For high cost of wire, the nodes organize into several distinct groups in space that correspond to network modules connected on a ring. In between, spatially and relationally modular small world networks are found.