Locating the source of diffusion in complex networks by time-reversal backward spreading

TL;DR

This paper introduces a time-reversal backward spreading algorithm for accurately locating the source of diffusion processes in complex networks using limited information, with broad applications in epidemic control and information spread.

Contribution

The authors develop a novel source localization algorithm and establish a general locatability condition applicable to various dynamical processes on complex networks.

Findings

Sources can be precisely located if the locatability condition is met.

The method is effective for epidemic spreading and consensus dynamics.

Application to H1N1 pandemic demonstrates practical utility.

Abstract

Locating the source that triggers a dynamical process is a fundamental but challenging problem in complex networks, ranging from epidemic spreading in society and on the Internet to cancer metastasis in the human body. An accurate localization of the source is inherently limited by our ability to simultaneously access the information of all nodes in a large-scale complex network. This thus raises two critical questions: how do we locate the source from incomplete information and can we achieve full localization of sources at any possible location from a given set of observable nodes. Here we develop a time-reversal backward spreading algorithm to locate the source of a diffusion-like process efficiently and propose a general locatability condition. We test the algorithm by employing epidemic spreading and consensus dynamics as typical dynamical processes and apply it to the H1N1 pandemic in China. We find that the sources can be precisely located in arbitrary networks insofar as the locatability condition is assured. Our tools greatly improve our ability to locate the source of diffusion in complex networks based on limited accessibility of nodal information. Moreover, they have implications for controlling a variety of dynamical processes taking place on complex networks, such as inhibiting epidemics, slowing the spread of rumors, pollution control and environmental protection.