This article aims to identify the partial topological structures of delayed complex network. Based on the drive-response concept, a more universal model, which includes nonlinear couplings, stochastic perturbations and multi-weights, is considered into drive-response networks. Different from previous methods, we obtain identification criteria by combining graph-theoretic method and adaptive synchronization. After that, the partial topological structures of stochastic multi-weighted complex networks with or without time delays can be identified successfully. Moreover, response network can reach synchronization with drive network. Ultimately, the effectiveness of the proposed theoretical results is validated through numerical simulations.