Hedgehog is an evolutionarily conserved developmental pathway, widely implicated in controlling various cellular responses such as cellular proliferation and stem cell renewal in human and other organisms, through external stimuli. Aberrant activation of this pathway in human adult stem cell line may cause different types of cancers. Hence, targeting this pathway in cancer therapy has become indispensable, but the non availability of detailed molecular interactions, complex regulations by extra- and intra-cellular proteins and cross talks with other pathways pose a serious challenge to get a coherent understanding of this signaling pathway for making therapeutic strategy. This motivated us to perform a computational study of the pathway and to identify probable drug targets. In this work, from available databases and literature, we reconstructed a complete hedgehog pathway which reports the largest number of molecules and interactions to date. Using recently developed computational techniques, we further performed structural and logical analysis of this pathway. In structural analysis, the connectivity and centrality parameters were calculated to identify the important proteins from the network. To capture the regulations of the molecules, we developed a master Boolean model of all the interactions between the proteins and created different cancer scenarios, such as Glioma, Colon and Pancreatic. We performed perturbation analysis on these cancer conditions to identify the important and minimal combinations of proteins that can be used as drug targets. From our study we observed the under expressions of various oncoproteins in Hedgehog pathway while perturbing at a time the combinations of the proteins GLI1, GLI2 and SMO in Glioma; SMO, HFU, ULK3 and RAS in Colon cancer; SMO, HFU, ULK3, RAS and ERK12 in Pancreatic cancer. This reconstructed Hedgehog signaling pathway and the computational analysis for identifying new combinatory drug targets will be useful for future in-vitro and in-vivo analysis to control different cancers.