One of the integral part of the network analysis is finding groups of nodes that exhibit similar properties. Community detection techniques are a popular choice to find such groups or communities within a network and it relies on graph-based methods to achieve this goal. Finding communities in biological networks such as gene co-expression networks are particularly important to find groups of genes where we can focus on further downstream analysis and find valuable insights regarding concerned diseases. Here, we present an effective community detection method called community detection using centrality-based approach (CDCA), designed using the graph centrality approach. The method has been tested using four benchmark bulk RNA-seq datasets for schizophrenia and bipolar disorder, and the performance has been proved superior in comparison to several other counterparts. The quality of communities are determined using intrinsic graph properties such as modularity and homogeneity. The biological significance of resultant communities is decided using the pathway enrichment analysis.