This letter presents a small-scale wireless distributed cooperative secure-communication network (WDCSN) design using a novel spectral graph FIR filter to achieve desired secrecy capacity at the intended receiver in the presence of single and multiple eavesdroppers. An undirected weighted graph \mathcal {G} (V, \mathcal {E}, W), with relays, eavesdroppers, source, and destination are as nodes (V), and circularly symmetric complex Gaussian random variables as edge weights (W) are considered to represent the WDCSN. A graph Laplacian is used as a graph shift operator to design the proposed filter. Filter coefficients are calculated by using the least squared error as a criterion. Simulations are conducted for a two-way WDCSN to achieve the desired secrecy capacity using different graph structures considered for WDCSN. The proposed filter design's performance is quantified by using the secrecy outage probability metric. The results show that desired secrecy capacity with SOP of 10^{-2} is achievable using the proposed methodology, irrespective of graph structures with variable complexity. An SOP performance gain of (60\!-\!80) \% is achieved over the SOP reported in the literature. © 2017 IEEE.