foremen ntioned hypergraph can be reduced into three bipartite graphs a graph holding the associations between actors and tags(AT), actors and items (AD) and tags and items(TD). For example, the AT valued bipartite graph defined as follows:AT:=(4A×T,Eat),Eat={(a,t)|i∈I:(a,t,i)∈E} Each such bipartite graph XY: =(XY, Exy) can be furthermore folded into two one-mode graphs Gx Ex), Gy =(Vy, Ew), where Vr =X V=Y, and Er={(a,b)|a,b∈X,y∈Y:(a,y)∈Exy,(b,y)∈Ery} Ey={(a,b)|a,b∈Y,丑x∈X:(x,a)∈Exy,(,b)∈Exy} We can furthermore define a weight of an edge eab E Ei in such a one-mode graph as u(eab):=|k|k∈K:(a,k)∈E1k,(b,k)∈Eik}. In other words, the weight w(ea. b) shows the number of times the a and b were linked together in an original bipartite graph By folding aforementioned bipartite graphs, we get six different one-mode graphs, each representing different semantic network encoded in the folksonomy. For example, by folding AT graph through tags, we get a social network of actors(users) based on overlapping sets of tags, where the links are bet people who have used the same tags with weights showing the number of tags they have used in common. Similarly, we can get a social network based on overlapping sets of items(two people are linked if they have tagged the same item, with weight showing the number of items they have tagged in common) In our work, we were primarily interested in folding TI graph through items giving us a semantic network of tags The proposed approach to creation of hierarchy from the folded folksonomy hypergraph as defined above is based on a rather simple assumptions of set theory In an ideal situation, the tag ta is a parent of tag tb if the set of entities (persons or items)classified under tb is a subset of the entities under ta In other words, all items classified under narrow tag also appear under the broader tag Moreover, since our goal was to produce a reusable hierarchy of hich could be mapped to users' interests and use this hierarchy as a basis for reasoning on those interests, we were not interested in tags, which were used only by a small amount of users, even if they were using it quite extensively. We wanted only what "crowd agrees upon"and were filtering-out tags not achieving a certain degree of popularity (i. e, it is not used by at least k% of all users), even if this decision reduced drastically the amount of tags in the resulting hierarchy The algorithm 1 shows the basic idea of our approach using a simple code. First, we create an artificial root of the hierarchy and put it in the set of already processed tags(ordered tags in the algorithm). Then, we process all tags from the folksonomy in the following manner 1. If the tag t does not reach the popularity threshold, we omit it immediately and n to the next one 2. Otherwise, we compute its overlap(intersect)with every tag from the ordered tags set, resulting in identifying the tag to with a maximum overlapThe aforementioned hypergraph can be reduced into three bipartite graphs: a graph holding the associations between actors and tags (AT), actors and items (AI) and tags and items (T I). For example, the AT valued bipartite graph is defined as follows: AT := hA × T, Eati, Eat = {(a, t) | ∃i ∈ I : (a, t, i) ∈ E}. Each such bipartite graph XY := hX × Y, Exyi can be furthermore folded into two one-mode graphs GX := hVx, Exi, GY := hVy, Eyi, where Vx = X, Vy = Y , and Ex = {(a, b) | a, b ∈ X, ∃y ∈ Y : (a, y) ∈ Exy, (b, y) ∈ Exy}, Ey = {(a, b) | a, b ∈ Y, ∃x ∈ X : (x, a) ∈ Exy, (x, b) ∈ Exy}. We can furthermore define a weight of an edge eab ∈ Ei in such a one-mode graph as w(eab) := |{k | k ∈ K : (a, k) ∈ Eik, (b, k) ∈ Eik}|. In other words, the weight w(ea,b) shows the number of times the a and b were linked together in an original bipartite graph. By folding aforementioned bipartite graphs, we get six different one-mode graphs, each representing different semantic network encoded in the folksonomy. For example, by folding AT graph through tags, we get a social network of actors (users) based on overlapping sets of tags, where the links are between people who have used the same tags with weights showing the number of tags they have used in common. Similarly, we can get a social network based on overlapping sets of items (two people are linked if they have tagged the same item, with weight showing the number of items they have tagged in common). In our work, we were primarily interested in folding T I graph through items, giving us a semantic network of tags. The proposed approach to creation of hierarchy from the folded folksonomy hypergraph as defined above is based on a rather simple assumptions of set theory: In an ideal situation, the tag ta is a parent of tag tb if the set of entities (persons or items) classified under tb is a subset of the entities under ta. In other words, all items classified under narrow tag also appear under the broader tag. Moreover, since our goal was to produce a reusable hierarchy of tags, which could be mapped to users’ interests and use this hierarchy as a basis for reasoning on those interests, we were not interested in tags, which were used only by a small amount of users, even if they were using it quite extensively. We wanted only what “crowd agrees upon” and were filtering-out tags not achieving a certain degree of popularity (i.e., it is not used by at least k% of all users), even if this decision reduced drastically the amount of tags in the resulting hierarchy. The algorithm 1 shows the basic idea of our approach using a simple pseudo￾code. First, we create an artificial root of the hierarchy and put it in the set of already processed tags (ordered tags in the algorithm). Then, we process all tags from the folksonomy in the following manner: 1. If the tag t does not reach the popularity threshold, we omit it immediately and pass on to the next one. 2. Otherwise, we compute its overlap (intersect) with every tag from the ordered tags set, resulting in identifying the tag to with a maximum overlap