A novel framework to analyze complex network dynamics
Matthieu Gilson, Nikos E Kouvaris, Gustavo Deco, Gorka Zamora-L\'opez

TL;DR
This paper introduces a comprehensive theoretical framework based on network response over time to analyze complex network dynamics, bridging structure and function through the Green function and flow concept.
Contribution
It proposes a novel, rigorous approach linking network topology and dynamics using the Green function, applicable to directed and weighted networks for various analyses.
Findings
Framework successfully applied to small-world and hierarchical networks
Relates to graph communicability and map equation concepts
Enables analysis of global network properties and community detection
Abstract
Graph theory constitutes a widely used and established field providing powerful tools for the characterization of complex networks. The intricate topology of networks can also be investigated by means of the collective dynamics observed in the interactions of self-sustained oscillations (synchronization patterns) or propagation-like processes such as random walks. However, networks are often inferred from real data forming dynamic systems, which are different from those employed to reveal their topological characteristics. This stresses the necessity for a theoretical framework dedicated to the mutual relationship between the structure and dynamics in complex networks, as the two sides of the same coin. Here we propose a rigorous framework based on the network response over time (i.e., Green function) to study interactions between nodes across time. For this purpose we define the…
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Taxonomy
TopicsOpinion Dynamics and Social Influence
