In collaborative indexing systems users generate a big amount of metadata by labelling web-based content. These labels are known as tags and form a shared vocabulary. In order to understand the characteristics of that vocabulary, we study structural patterns of these tags by implying the theory of self-organizing systems. Therefore, we utilize the graph theoretic notion to model the network of tags and their valued connections, which represent frequency rates of co-occurring tags. Empirical data is provided by the free-for-all collaborative indexing systems Delicious, Connotea and CiteULike. First, we measure the frequency distribution of co-occurring tags. Secondly, we correlate these tags towards their rank over time. Results indicate a strong relationship among a few tags as well as a notable persistence of these tags over time. Therefore, we make the educated guess that the observed collaborative indexing systems are self-organizing systems towards a shared vocabulary building. Imp...