Table 1. Quality measures for the reconstructed hierarchies in case of the protein function data set.

algorithm A	21%	66%	2%	32%	0%	35%	78%
algorithm B	20%	52%	3%	44%	1%	30%	75%
P. Heymann & H. Garcia-Molina	19%	51%	3%	46%	0%	30%	75%
P. Schmitz	18%	65%	2%	23%	10%	30%	75%

The quality of the tag hierarchy obtained for the tagged protein data set, , was evaluated by comparing it to the hierarchy of protein functions in the Gene Ontology, . The quality measures presented in the different columns are the following: the ratio of exactly matching links in ,denoted by , the ratio of acceptable links, , (connecting more distant ancestor-descendant pairs), the ratio of inverted links, , (pointing in the opposite direction), the ratio of unrelated links, , (connecting tags on different branches in ), the ratio of missing links in , denoted by , the normalized mutual information between the two hierarchies, , and the linearized mutual information, , corresponding to the fraction of exactly matching links remaining after a random link rewiring process stopped at NMI value given by . The different rows correspond to results obtained from algorithm A (1 row), algorithm B (2 row),the method by P. Heymann & H. Garcia-Molina (3 row), and the algorithm by P. Schmitz (4 row).