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It is important to incorporate the accumulated biological pathways and interactions knowledge into genome-wide association studies to elucidate correlations between genetic variants and disease. Although a number of methods have been developed recently to identify disease related genes using prior biological knowledge, most methods only encourage the smoothness of the coefficients along the network which does not address the case where two connected genes both have positive or negative effects on the response. To overcome this issue, we propose to apply the Laplacian operation on the absolute values of the coefficients to take account of the positive and negative effects as well as a L1 norm term to impose sparsity. Further, an efficient algorithm is developed to get the whole solution path. Simulation studies show that the proposed method has better performance than network-constrained regularisation without absolute values. Applying our method on a microarray data of Alzheimer's disease AD identifies several subnetworks on Kyoto Encyclopedia of Genes and Genomes KEGG transcriptional pathways that are related to progression of AD. Many of those findings are confirmed by published literature.