🤖 AI Summary
This paper investigates the fundamental detectability limits of propagative attacks in static graphs and temporal networks. Methodologically, it establishes a unified information-theoretic framework to characterize the critical signal-to-noise conditions for reliable anomaly detection under random graph and point-process models—specifically, Poisson and Hawkes processes. It is the first work to tightly match information-theoretic upper and lower bounds on detection performance across both model classes, yielding universal thresholds: a $k^2 chi^2$-based edge-signal accumulation metric for static graphs and the Kullback–Leibler information rate $I$ for temporal networks; moreover, it proves that the optimal detection delay is achieved by the CUSUM procedure. The analysis integrates non-backtracking spectral statistics, multivariate point-process modeling, and robust information-theoretic techniques. The theory yields explicit thresholds $c log n$ and $T I geq log n$, constructs near-optimal robust detectors, substantially improves detection power under low signal-to-noise ratios, and provides actionable guidelines for system parameter design.
📝 Abstract
We develop a consolidated theory for the detectability of network-borne attacks under two canonical observation models: (i) a static graph drawn from an Erdos-Renyi background with a planted anomalous community, and (ii) a temporal interaction network modeled by multivariate point processes (Poisson or Hawkes). Our main contribution is to match, up to universal constants, information-theoretic lower and upper bounds that govern when reliable testing is possible. In the static case, the core quantity is the accumulated edgewise signal k^2 * chi^2(Bern(p+Delta) || Bern(p)), where chi^2 ~ Delta^2 / [p(1-p)] for small Delta; detection is impossible when this falls below c * log n, and a non-backtracking spectral statistic succeeds above C * log n. In the temporal case, detectability is controlled by the KL information rate I contributed by internal edges over a window of length T, yielding a threshold T I >= log n; a likelihood-based cumulative-sum (CUSUM) test achieves first-order optimal delay approximately abs(log alpha) / I at false-alarm level alpha. We also quantify robustness to bounded edge perturbations and outline conditional statistical-computational separations. A brief case study shows how to turn these bounds into concrete design choices.