The problem of community detection has recently been studied widely in the context of the web and social media networks. Most algorithms for community detection assume that the entire network is available for online analysis. In practice, this is not really true, because only restricted portions of the network may be available at any given time for analysis. Many social networks such as Facebook have privacy constraints, which do not allow the discovery of the entire structure of the social network. Even in the case of more open networks such as Twitter, it may often be challenging to crawl the entire network from a practical perspective. For many other scenarios such as adversarial networks, the discovery of the entire network may itself be a costly task, and only a small portion of the network may be discovered at any given time. Therefore, it can be useful to investigate whether network mining algorithms can integrate the network discovery process tightly into the mining process, so that the best results are achieved for particular constraints on discovery costs. In this context, we will discuss algorithms for integrating community detection with network discovery. We will tightly integrate with the cost of actually discovering a network with the community detection process, so that the two processes can support each other and are performed in a mutually cohesive way. We present experimental results illustrating the advantages of the approach.