Unveiling the Relationship Between Structure and Dynamics in Complex Networks

TL;DR

This paper introduces a new framework to analyze how the structure of complex networks influences the diverse dynamics of different node groups, surpassing traditional average-based methods.

Contribution

A novel framework is proposed to identify principal dynamic features and their dependence on network structure, applied to three models to reveal structured, group-specific dynamics.

Findings

Different node groups exhibit specific dynamics influenced by network structure

The approach reveals highly structured, group-specific behaviors in network models

Traditional average-based analyses overlook diverse local dynamics

Abstract

Over the last years, a great deal of attention has been focused on complex networked systems, characterized by intricate structure and dynamics. The latter has been often represented in terms of overall statistics (e.g. average and standard deviations) of the time signals. While such approaches have led to many insights, they have failed to take into account that signals at different parts of the system can undergo distinct evolutions, which cannot be properly represented in terms of average values. A novel framework for identifying the principal aspects of the dynamics and how it is influenced by the network structure is proposed in this work. The potential of this approach is illustrated with respect to three important models (Integrate-and-Fire, SIS and Kuramoto), allowing the identification of highly structured dynamics, in the sense that different groups of nodes not only presented specific dynamics but also felt the structure of the network in different ways.