Detecting link failures in complex network processes using remote monitoring

We study whether local structural changes in a complex network can be distinguished from passive remote time-course measurements of the network´s dynamics. Specifically the detection of link failures in a network synchronization process from noisy measurements at a single network component is considered. By phrasing the detection task as a Maximum A Posteriori Probability hypothesis testing problem, we are able to obtain conditions under which the detection is 1) improved over the a priori and 2) asymptotically perfect, in terms of the network spectrum and graph. We find that, in the case where the detector has knowledge of the network´s state, perfect detection is possible under general connectivity conditions regardless of the measurement location. When the detector does not have state knowledge, a remote signature permits improved but not perfect detection, under the same connectivity conditions. At its essence, detectability is achieved because of the close connection between a network´s topology, its eigenvalues and local response characteristics.