Pathway analyses are playing an increasingly important role in understanding biological mechanism, cellular function and disease states. Current pathway-identification methods generally focus on only the changes of gene expression levels; however, the biological relationships among genes are also the fundamental components of pathways, and the dysregulated relationships may also alter the pathway activities. We propose a powerful computational method, Edge Set Enrichment Analysis (ESEA), for the identification of dysregulated pathways. This provides a novel way of pathway analysis by investigating the changes of biological relationships of pathways in the context of gene expression data. Simulation studies illustrate the power and performance of ESEA under various simulated conditions. Using real datasets from p53 mutation, Type 2 diabetes and lung cancer, we validate effectiveness of ESEA in identifying dysregulated pathways. We further compare our results with five other pathway enrichment analysis methods. With these analyses, we show that ESEA is able to help uncover dysregulated biological pathways underlying complex traits and human diseases via specific use of the dysregulated biological relationships. We develop a freely available R-based tool of ESEA. Currently, ESEA can support pathway analysis of the seven public databases (KEGG; Reactome; Biocarta; NCI; SPIKE; HumanCyc; Panther).