The link structure of the Web is generally viewed as the webgraph, and web structure mining is a research area that mainly aims to find hidden communities in the Web and so on, by focusing on the webgraph. In this paper, we identify a common frequent substructure by observing the webgraph, and newly define it as an isolated star (i-star). We propose an efficient enumeration algorithm of i-stars, and try structure mining by enumerating them from the real web data. As a result, we observed that most of i-stars correspond to index structures in single domains, while some of them are verified to stand for useful communities, which implies the validity of i-stars as candidate substructure for structure mining. We also suggest that the notion of i-star can be a helpful tool for preprocessing the webgraph to have its succinct representation for further structure mining.