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We propose a new method for characterizing the dynamics of complex networks with its application to the link prediction problem. Our approach is based on the discovery of network sub graphs (in this study: triads of nodes) and measuring their transitions during network evolution. We define the Triad Transition Matrix (TTM) containing the probabilities of transitions between triads found in the network, then we show how it can help to discover and quantify the dynamic patterns of network evolution. We also propose the application of TTM to link prediction with an algorithm (called TTM-predictor) which shows good performance, especially for sparse networks analyzed in short time scales. The future applications and research directions of our approach are also proposed and discussed.