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Design of video storyboards, which enables a user to access any video in a friendly and meaningful way, has emerged as an important area of research in the multimedia community. In this paper, we propose a novel semi-automated method for construction of video storyboards based on Delaunay graphs. A robust edge pruning strategy, where the edge weights are assumed to follow a Gaussian distribution, is applied on an appropriately constructed Delaunay graph. The proposed method also takes into account two advanced user needs, namely the waiting time and the number of frames an user wants to see in the story board Experimental results on some standard videos of different genre clearly indicate the superiority of the proposed method in terms of the F0.5 measure.