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This paper presents a novel methodology for social network discovery based on the sensitivity coefficients of importance metrics, namely the Markov centrality of a node, a metric based on random walks. Analogous to node importance, which ranks the important nodes in a social network, the sensitivity analysis of this metric provides a ranking of the relationships between nodes. The sensitivity parameter of the importance of a node with respect to another measures the direct or indirect impact of a node. We show that these relationships help discover hidden links between nodes and highlight meaningful links between seemingly disparate sub-networks in a social structure. We introduce the notion of implicit links, which represent an indirect relationship between nodes not connected by edges, seen as hidden connections in complex networks. We demonstrate our methodology on two social network data sets and use sensitivity-guided visualizations to highlight our findings. Our results show that this analytic tool, when coupled with visualization, is an effective mechanism for discovering social networks.