h i g h l i g h t s• We study detection of network changes from remote noisy time-series measurements.• A Maximum A-Posteriori Probability hypothesis testing scheme is employed.• Relationships between the network topology and MAP detector performance are developed. • Detector performance depends on presence of certain paths in the network. • Simulations demonstrate the analytical results developed. a b s t r a c tWe 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.

We characterize the vulnerability of a linear network synchronization process to intrusion by an adversary that can actuate a single network component. Specifically, we model the intruder as seeking to move the state of the synchronization process to an undesirable value or set (which may or may not be known to system operators) via a local actuation. We evaluate the network vulnerability in terms of the whether or not the intruder can achieve its goal, and also the minimum actuation energy (or expected minimum energy, if the goal is unknown) required of the adversary to achieve the goal. We formalize that the required energy is related to the inverse of the controllability Gramian for the process, and statistics defined thereof (e.g., its trace and determinant). We then obtain explicit formulas for the Gramian inverse and its associated statistics. These explicit formulae yield interesting structural and graphtheoretic characterizations of the energy-based vulnerability measures.

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