Detection of non-overlapping and overlapping communities are essentially the same problem. However, current algorithms focus either on finding overlapping or non-overlapping communities. We present a generalized framework that can identify both non-overlapping and overlapping communities, without any prior input about the network or its community distribution. To do so, we introduce a vertex-based metric, GenPerm, that quantifies by how much a vertex belongs to each of its constituent communities. Our community detection algorithm is based on maximizing the GenPerm over all the vertices in the network. We demonstrate, through experiments over synthetic and real-world networks, that GenPerm is more effective than other metrics in evaluating community structure. Further, we show that due to its vertex-centric property, GenPerm can be used to unfold several inferences beyond community detection, such as core-periphery analysis and message spreading. Our algorithm for maximizing GenPerm outperforms six state-of-the-art algorithms in accurately predicting the ground-truth labels. Finally, we discuss the problem of resolution limit in overlapping communities and demonstrate that maximizing GenPerm can mitigate this problem.