Reconstructing propagation networks with natural diversity and identifying hidden sources

TL;DR

This paper introduces a compressed sensing framework for reconstructing complex network structures and dynamics from limited data, enabling identification of hidden sources and improving understanding of spreading processes.

Contribution

The authors develop a novel compressed sensing-based method for reconstructing stochastic network dynamics and locating hidden sources from minimal binary data.

Findings

Full network reconstruction is possible with limited polarized data.

Hidden sources triggering spreading can be identified without direct observation.

Method applies successfully to model and real-world networks.

Abstract

Our ability to uncover complex network structure and dynamics from data is fundamental to understanding and controlling collective dynamics in complex systems. Despite recent progress in this area, reconstructing networks with stochastic dynamical processes from limited time series remains to be an outstanding problem. Here we develop a framework based on compressed sensing to reconstruct complex networks on which stochastic spreading dynamics take place. We apply the methodology to a large number of model and real networks, finding that a full reconstruction of inhomogeneous interactions can be achieved from small amounts of polarized (binary) data, a virtue of compressed sensing. Further, we demonstrate that a hidden source that triggers the spreading process but is externally inaccessible can be ascertained and located with high confidence in the absence of direct routes of propagation from it. Our approach thus establishes a paradigm for tracing and controlling epidemic invasion and information diffusion in complex networked systems.