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We propose a time\u2010dependent undirected graphical model that ensures temporal and structural smoothness across time\u2010specific networks to examine the trajectories of interactions between markers aligned at the time of disease onset. Specifically, we anchor subjects relative to the time of disease diagnosis (anchoring time) as in a revival process, and we estimate networks at each time point of interest relative to the anchoring time. To use all available data, we apply kernel weights to borrow information across observations that are close to the time of interest. Adaptive lasso weights are introduced to encourage temporal smoothness in edge strength, while a novel elastic fused\u2010 penalty removes spurious edges and encourages temporal smoothness in network structure. Our approach can handle practical complications such as unbalanced visit times. We conduct simulation studies to compare our approach with existing methods. 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