There exist many tools and methods for construction of co-expression network from gene expression data and for extraction of densely connected gene modules. In this paper, a method is introduced to construct co-expression network and to extract co-expressed modules having high biological significance. The proposed method has been validated on several well known microarray datasets extracted from a diverse set of species, using statistical measures, such as p and q values. The modules obtained in these studies are found to be biologically significant based on Gene Ontology enrichment analysis, pathway analysis, and KEGG enrichment analysis. Further, the method was applied on an Alzheimer's disease dataset and some interesting genes are found, which have high semantic similarity among them, but are not significantly correlated in terms of expression similarity. Some of these interesting genes, such as MAPT, CASP2, and PSEN2, are linked with important aspects of Alzheimer's disease, such as dementia, increase cell death, and deposition of amyloid-beta proteins in Alzheimer's disease brains. The biological pathways associated with Alzheimer's disease, such as, Wnt signaling, Apoptosis, p53 signaling, and Notch signaling, incorporate these interesting genes. The proposed method is evaluated in regard to existing literature.