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Network representation has steadily gained in popularity over the past decades. In many disciplines such as finance, genetics, neuroscience or human travel to cite a few, the network may not directly be observable and needs to be inferred from time-series data, leading to the issue of separating direct interactions between two entities forming the network from indirect interactions coming through its remaining part. Drawing on recent contributions proposing strategies to deal with this problem such as the so-called “global silencing” approach of Barzel and Barabasi or “network deconvolution” of Feizi et al. (2013), we propose a novel methodology to infer an effective network structure from multivariate conditional information transfers. Its core principal is to test the information transfer between two nodes through a step-wise approach by conditioning the transfer for each pair on a specific set of relevant nodes as identified by our algorithm from the rest of the network. The methodology is model free and can be applied to high-dimensional networks with both inter-lag and intra-lag relationships. It outperforms state-of-the-art approaches for eliminating the redundancies and more generally retrieving simulated artificial networks in our Monte-Carlo experiments. We apply the method to stock market data at different frequencies (15 min, 1 h, 1 day) to retrieve the network of US largest financial institutions and then document how bank’s centrality measurements relate to bank’s systemic vulnerability.