Small Worlds in Space: Synchronization, 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.