Conventional community detection methods often categorize all nodes into clusters. However, the presumed community structure of interest may only be valid for a subset of nodes (named as `tight nodes'), while the rest of the network may consist of noninformative ``scattered nodes''. For example, a protein-protein network often contains proteins that do not belong to specific biological functional modules but are involved in more general processes, or act as bridges between different functional modules. Forcing each of these proteins into a single cluster introduces unwanted biases and obscures the underlying biological implication. To address this issue, we propose a tight community detection (TCD) method to identify tight communities excluding scattered nodes. The algorithm enjoys a strong theoretical guarantee of tight node identification accuracy and is scalable for large networks. The superiority of the proposed method is demonstrated by various synthetic and real experiments.

Local clustering aims at extracting a local structure inside a graph without the necessity of knowing the entire graph structure. As the local structure is usually small in size compared to the entire graph, one can think of it as a compressive sensing problem where the indices of target cluster can be thought as a sparse solution to a linear system. In this paper, we apply this idea based on two pioneering works under the same framework and propose a new semi-supervised local clustering approach using only few labeled nodes. Our approach improves the existing works by making the initial cut to be the entire graph and hence overcomes a major limitation of the existing works, which is the low quality of initial cut. Extensive experimental results on various datasets demonstrate the effectiveness of our approach.