Comparing the hierarchy of author given tags and repository given tags in a large document archive

Folksonomies - large databases arising from collaborative tagging of items by independent users - are becoming an increasingly important way of categorizing information. In these systems users can tag items with free words, resulting in a tripartite item-tag-user network. Although there are no prescribed relations between tags, the way users think about the different categories presumably has some built in hierarchy, in which more special concepts are descendants of some more general categories. Several applications would benefit from the knowledge of this hierarchy. Here we apply a recent method to check the differences and similarities of hierarchies resulting from tags given by independent individuals and from tags given by a centrally managed repository system. The results from out method showed substantial differences between the lower part of the hierarchies, and in contrast, a relatively high similarity at the top of the hierarchies.Comment: 10 page

Extracting tag hierarchies

Tagging items with descriptive annotations or keywords is a very natural way to compress and highlight information about the properties of the given entity. Over the years several methods have been proposed for extracting a hierarchy between the tags for systems with a "flat", egalitarian organization of the tags, which is very common when the tags correspond to free words given by numerous independent people. Here we present a complete framework for automated tag hierarchy extraction based on tag occurrence statistics. Along with proposing new algorithms, we are also introducing different quality measures enabling the detailed comparison of competing approaches from different aspects. Furthermore, we set up a synthetic, computer generated benchmark providing a versatile tool for testing, with a couple of tunable parameters capable of generating a wide range of test beds. Beside the computer generated input we also use real data in our studies, including a biological example with a pre-defined hierarchy between the tags. The encouraging similarity between the pre-defined and reconstructed hierarchy, as well as the seemingly meaningful hierarchies obtained for other real systems indicate that tag hierarchy extraction is a very promising direction for further research with a great potential for practical applications.Comment: 25 pages with 21 pages of supporting information, 25 figure

Overlapping modularity at the critical point of k-clique percolation

One of the most remarkable social phenomena is the formation of communities in social networks corresponding to families, friendship circles, work teams, etc. Since people usually belong to several different communities at the same time, the induced overlaps result in an extremely complicated web of the communities themselves. Thus, uncovering the intricate community structure of social networks is a non-trivial task with great potential for practical applications, gaining a notable interest in the recent years. The Clique Percolation Method (CPM) is one of the earliest overlapping community finding methods, which was already used in the analysis of several different social networks. In this approach the communities correspond to k-clique percolation clusters, and the general heuristic for setting the parameters of the method is to tune the system just below the critical point of k-clique percolation. However, this rule is based on simple physical principles and its validity was never subject to quantitative analysis. Here we examine the quality of the partitioning in the vicinity of the critical point using recently introduced overlapping modularity measures. According to our results on real social- and other networks, the overlapping modularities show a maximum close to the critical point, justifying the original criteria for the optimal parameter settings.Comment: 20 pages, 6 figure

Élőlények kollektív viselkedésének statisztikus fizikája = Statistical physics of the collective behaviour of organisms

Experiments: We have carried out quantitative experiments on the collective motion of cells as a function of their density. A sharp transition could be observed from the random motility in sparse cultures to the flocking of dense islands of cells. Using ultra light GPS devices developed by us, we have determined the existing hierarchical relations within a flock of 10 homing pigeons. Modelling: From the simulations of our new model of flocking we concluded that the information exchange between particles was maximal at the critical point, in which the interplay of such factors as the level of noise, the tendency to follow the direction and the acceleration of others results in large fluctuations. Analysis: We have proposed a novel link-density based approach to finding overlapping communities in large networks. The algorithm used for the implementation of this technique is very efficient for most real networks, and provides full statistics quickly. Correspondingly, we have developed a by now popular, user-friendly, freely downloadable software for finding overlapping communities. Extending our method to the time-dependent regime, we found that large groups in evolving networks persist for longer if they are capable of dynamically altering their membership, thus, an ability to change the group composition results in better adaptability. We also showed that knowledge of the time commitment of members to a given community can be used for estimating the community's lifetime. Experiments: We have carried out quantitative experiments on the collective motion of cells as a function of their density. A sharp transition could be observed from the random motility in sparse cultures to the flocking of dense islands of cells. Using ultra light GPS devices developed by us, we have determined the existing hierarchical relations within a flock of 10 homing pigeons. Modelling: From the simulations of our new model of flocking we concluded that the information exchange between particles was maximal at the critical point, in which the interplay of such factors as the level of noise, the tendency to follow the direction and the acceleration of others results in large fluctuations. Analysis: We have proposed a novel link-density based approach to finding overlapping communities in large networks. The algorithm used for the implementation of this technique is very efficient for most real networks, and provides full statistics quickly. Correspondingly, we have developed a by now popular, user-friendly, freely downloadable software for finding overlapping communities. Extending our method to the time-dependent regime, we found that large groups in evolving networks persist for longer if they are capable of dynamically altering their membership, thus, an ability to change the group composition results in better adaptability. We also showed that knowledge of the time commitment of members to a given community can be used for estimating the community's lifetime

Asymptotics of high order noise corrections

We consider an evolution operator for a discrete Langevin equation with a strongly hyperbolic classical dynamics and noise with finite moments. Using a perturbative expansion of the evolution operator we calculate high order corrections to its trace in the case of a quartic map and Gaussian noise. The leading contributions come from the period one orbits of the map. The asymptotic behaviour is investigated and is found to be independent up to a multiplicative constant of the distribution of noise.Comment: 5 pages, 6 figures, submitted to J. Stat. Phy

Komplex hálózatok vizsgálata = Studies of complex networks

Kifejlesztettünk egy módszert a hálózati Hamilton-függvény visszafejtésére az élek átrendeződési folyamataiból. A vizsgált hálózatok Hamilton-függvényei egy univerzális alakot követnek, mely konzisztens a preferenciális kapcsolódási szabállyal. Kifejlesztettünk egy új hálózati csoportkereső módszert, melynél a feltárt csoportok egy-egy k-klikk perkolációs klaszternek felelnek meg. Az így definiált csoport felosztás nagy előnye a hogy megengedi a csoportok közti átfedéseket. Az átfedések révén természetes módon származtatható a csoportok hálózata is, melynek révén a rendszert egy magasabb (hierarchikus) szerveződési szinten tanulmányozhatjuk. A vizsgált nagy méretű hálózatok esetén a csoporthálózat fokszámeloszlása hatványszerűen cseng le. A csoporthálózat időbeli növekedése a preferenciális kapcsolódási szabálynak megfelelően zajlik. Az élesztő baktérium fehérje kölcsönhatási hálózatában az általunk feltárt csoportok jelentős része egy-egy jól beazonosítható fehérje funkciónak feleltethető meg. Ez alapján módszerünk lehetővé teszi a sejtműködésben eddig ismeretlen szerepű fehérjék funkciójának jóslását a feltárt csoportokhoz való tartozás alapján. A hálózati csoportkeresőhöz egy ingyenesen letölthető grafikus kezelőfelületet is készítettünk, mely a csoportok megkeresése mellet képes azok megjelenítésére, illetve a csoportok hálózatában való navigálásra, keresésre. | We have developed a reverse engineering method to deduce the Hamilton-function of networks from the restructuring of the links. The energy function in the studied networks followed a universal form, which was consistent with the preferential attachment rule. We have developed a new community finding method defining the communities as k-clique percolation clusters. The advantage of this approach is that it allows overlaps between the communities. We can also define the graph of communities based on the overlaps in a natural way. With the help of the community graph we can study the hierarchical organization of the system at a higher level. In the studied large networks the degree distribution of the graph of communities decays as a power-law. The time development of the graph of communities is governed by the preferential attachment rule. The majority of the communities obtained with our method in case of the protein interaction network of the yeast bacteria can be associated with a well defined protein function. According to that, our method can be used for function prediction in case of unknown proteins based on community membership. We developed freely downloadable software capable of locating and visualizing the communities (and the graph of communities) in networks