Many real world datasets are represented in the form of graphs. The classical graph properties found in the data, like cliques or independent sets, can reveal new interesting information in the data. However, such properties can be either too rare or too trivial in the given context. By relaxing the criteria of the classical properties, we can find more and totally new patterns in the data. In this paper, we define relaxed graph properties and study their use in analyzing and processing graph-based data. Especially, we consider the problem of finding self-referring groups in WWW, and give a general algorithm for mining all such patterns from a collection of WWW pages. We suggest that such self-referring groups can reveal web communities or other clusterings in WWW and also help in compression of graph-formed data.