Detecting and analyzing dense subgroups or communities from social and information networks has attracted great attention over last decade due to its enormous applicability in various domains. A number of approaches have been made to solve this challenging problem using different quality functions and data structures. A number of cohesive structures have been defined as a primary element for community discovery in networks. Unfortunately, most of these structures suffer from computational intractability and they fail to mine meaningful communities from real-world graphs. The main objective of the paper is to exploit some cohesive structures in one unified framework to detect high-quality communities in networks. First, we revisit some existing subgraph models by showing their limits in terms of cohesiveness, which is an elementary aspect in graph theory. Next, to make these structures more effective models of communities, we focus on interesting configurations that are larger and more densely connected by fulfilling some new constraints. The new structures allow to ensure a larger density on the discovered clusters and overcome the weaknesses of the existing structures. The performance studies demonstrate that our approach significantly outperform state-of-the-art techniques for computing overlapping communities in real-world networks by several orders of magnitude.