19.4.2.2 FolkRank
The web search algorithm PageRank [2] reflects the idea that a web page is important if there are many pages linking to it, and if those pages are important themselves. 12 In [12], Hotho et al. employed the same underlying principle for Googlelike search and ranking in folksonomies. The key idea of the FolkRank algorithm is that a resource which is tagged with important tags by important users becomes important itself. The same holds, symmetrically, for tags and users. We have thus a graph of vertices which are mutually reinforcing each other by spreading their weights. In this section we briefly recall the principles of the FolkRank algorithm, and explain how it can be used for generating tag recommendations.
Because of the different nature of folksonomies compared to the web graph (undirected triadic hyperedges instead of directed binary edges), PageRank cannot be applied directly on folksonomies. In order to employ a weight-spreading ranking scheme on folksonomies, we overcome this problem in two steps. First, we transform the hypergraph into an undirected graph. Then we apply a differential ranking approach that deals with the skewed structure of the network and the undirectedness of folksonomies, and which allows for topic-specific rankings.