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This paper investigates the problem of securing k source symbols transmission in a network with side information to an adversary who can obtain k' source symbols, eavesdrop μ channels and contaminate d channels. We characterize the security performance of the new model by relative network generalized Hamming weight (RNGHW) of a linear code and a subcode with respect to network error correction (NEC). The model regards secure network coding on wiretap networks as a special case. An upper bound on NEC-RNGHW is introduced and two deterministic constructions of transmission scheme are proposed to achieve the bound.