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We present a novel framework to represent sets of time-varying signals as dynamic graphs using the non-negative kernel (NNK) graph construction. We extend the original NNK framework to allow explicit delays as part of the graph construction, so that unlike in NNK, two nodes can be connected with an edge corresponding to a non-zero time delay, if there is higher similarity between the signals after shifting one of them. We also propose to characterize the similarity between signals at different nodes using the node degree and clustering coefficients of their respective visibility graphs. Graph edges that can representing temporal delays, we provide a new perspective that enables us to see the effect of synchronization in graph construction for time-series signals. For both temperature and EEG datasets, we show that our proposed approach can achieve sparse and interpretable graph representations. Furthermore, the proposed method can be useful in characterizing different EEG experiments using sparsity.