Discovering the relationships of gene to gene, gene to its related diseases, and diseases implicated in common genes is important. However, traditional biological methods can be expensive. Here, we show that the diseases implicated in common genes and the genes related to a multiple-gene disease can be inferred by the vertex similarity measures, a type of method to find the similar vertices in a network based on its structure. The relationship among diseases and the relationship among genes are modeled as two biological networks: human disease network and disease gene network. We apply the vertex similarity among the vertices in the human disease network to infer the diseases implicated in common genes. By similar manner, we utilize vertex similarity measures on the disease gene network to infer the genes related to a common multiple-gene disease. Experimental results demonstrate the potential of vertex similarity as an inexpensive approach to infer the possible links between genes and between diseases. We also develop a system to visualize and get a better understanding about the relationships among diseases and genes.