  Preserving the topology from being inferred by external adversaries has
become a paramount security issue for network systems (NSs), and adding random
noises to the nodal states provides a promising way. Nevertheless, recent works
have revealed that the topology cannot be preserved under i.i.d. noises in the
asymptotic sense. How to effectively characterize the non-asymptotic
preservation performance still remains an open issue. Inspired by the deviation
quantification of concentration inequalities, this paper proposes a novel
metric named trace-based variance-expectation ratio. This metric effectively
captures the decaying rate of the topology inference error, where a slower rate
indicates better non-asymptotic preservation performance. We prove that the
inference error will always decay to zero asymptotically, as long as the added
noises are non-increasing and independent (milder than the i.i.d. condition).
Then, the optimal noise design that produces the slowest decaying rate for the
error is obtained. More importantly, we amend the noise design by introducing
one-lag time dependence, achieving the zero state deviation and the non-zero
topology inference error in the asymptotic sense simultaneously. Extensions to
a general class of noises with multi-lag time dependence are provided.
Comprehensive simulations verify the theoretical findings.
