Predicting the patterns of spatio-temporal signal propagation in complex networks

TL;DR

This paper develops a formal framework to predict how signals propagate through complex networks, revealing three universal classes of dynamic behavior that depend on network structure and interaction mechanisms.

Contribution

It introduces a systematic method to translate network topology into spatio-temporal signal propagation patterns across diverse nonlinear dynamic models.

Findings

Propagation rules condense into three universal classes.

The framework applies to real-world networks like social and cellular systems.

Predicts diverse phenomena such as virus spread and genetic information transfer.

Abstract

A major achievement in the study of complex networks is the observation that diverse systems, from sub-cellular biology to social networks, exhibit universal topological characteristics. Yet this universality does not naturally translate to the dynamics of these systems , hindering our progress towards a general theoretical framework of network dynamics. The source of this theoretical gap is the fact that the behavior of a complex system cannot be uniquely predicted from its topology, but rather depends also on the dynamic mechanisms of interaction between the nodes, hence systems with similar structure may exhibit profoundly different dynamic behavior. To bridge this gap, we derive here the patterns of network information transmission, indeed, the essence of a network's behavior, by offering a systematic translation of topology into the actual spatio-temporal propagation of perturbative signals. We predict, for an extremely broad range of nonlinear dynamic models, that the propagation rules condense around three highly distinctive dynamic universality classes, characterized by the interplay between network paths, degree distribution and the interaction dynamics. Our formalism helps us leverage the major advances in the mapping of real world networks, into predictions on the actual dynamic propagation, from the spread of viruses in social networks to the discussion of genetic information in cellular systems.