arXiv subjects

Gergely Palla

Publications and source records attributed to Gergely Palla.

At least 37 records · Page 2Linked to original sources

arXiv2019

Time evolution of the hierarchical networks between PubMed MeSH terms

Hierarchical organisation is a prevalent feature of many complex networks appearing in nature and society. A relating interesting, yet less studied question is how does a hierarchical network evolve over time? Here we take a data driven approach and examine the time evolution of the network between the Medical Subject Headings (MeSH) provided by the National Center for Biotechnology Information (NCBI, part of the U. S. National Library of Medicine). The network between the MeSH terms is organised into 16 different, yearly updated hierarchies such as "Anatomy", "Diseases", "Chemicals and Drugs", etc. The natural representation of these hierarchies is given by directed acyclic graphs, composed of links pointing from nodes higher in the hierarchy towards nodes in lower levels. Due to the yearly updates, the structure of these networks is subject to constant evolution: new MeSH terms can appear, terms becoming obsolete can be deleted or be merged with other terms, and also already existing parts of the network may be rewired. We examine various statistical properties of the time evolution, with a special focus on the attachment and detachment mechanisms of the links, and find a few general features that are characteristic for all MeSH hierarchies. According to the results, the hierarchies investigated display an interesting interplay between non-uniform preference with respect to multiple different topological and hierarchical properties.

physics.soc-ph↗

arXiv2019

Generalised thresholding of hidden variable network models with scale-free property

The hidden variable formalism (based on the assumption of some intrinsic node parameters) turned out to be a remarkably efficient and powerful approach in describing and analyzing the topology of complex networks. Owing to one of its most advantageous property - namely proven to be able to reproduce a wide range of different degree distribution forms - it has become a standard tool for generating networks having the scale-free property. One of the most intensively studied version of this model is based on a thresholding mechanism of the exponentially distributed hidden variables associated to the nodes (intrinsic vertex weights), which give rise to the emergence of a scale-free network where the degree distribution $p(k)\sim k^{-γ}$ is decaying with an exponent of $γ=2$. Here we propose a generalization and modification of this model by extending the set of connection probabilities and hidden variable distributions that lead to the aforementioned degree distribution, and analyze the conditions leading to the above behavior analytically. In addition, we propose a relaxation of the hard threshold in the connection probabilities, which opens up the possibility for obtaining sparse scale free networks with arbitrary scaling exponent.

physics.soc-ph↗

arXiv2019

Emergence of leader-follower hierarchy among players in an on-line experiment

Hierarchical networks are prevalent in nature and society, corresponding to groups of actors - animals, humans or even robots - organised according to a pyramidal structure with decision makers at the top and followers at the bottom. While this phenomenon is seemingly universal, the underlying governing principles are poorly understood. Here we study the emergence of hierarchies in groups of people playing a simple dot guessing game in controlled experiments, lasting for about 40 rounds, conducted over the Internet. During the games, the players had the possibility to look at the answer of a limited number of other players of their choice. This act of asking for advice defines a directed connection between the involved players, and according to our analysis, the initial random configuration of the emerging networks became more structured overt time, showing signs of hierarchy towards the end of the game. In addition, the achieved score of the players appeared to be correlated with their position in the hierarchy. These results indicate that under certain conditions imitation and limited knowledge about the performance of other actors is sufficient for the emergence of hierarchy in a social group.

physics.soc-ph↗

arXiv2018

Phase space volume scaling of generalized entropies and anomalous diffusion scaling governed by corresponding non-linear Fokker-Planck equations

Many physical, biological or social systems are governed by history-dependent dynamics or are composed of strongly interacting units, showing an extreme diversity of microscopic behaviour. Macroscopically, however, they can be efficiently modeled by generalizing concepts of the theory of Markovian, ergodic and weakly interacting stochastic processes. In this paper, we model stochastic processes by a family of generalized Fokker-Planck equations whose stationary solutions are equivalent to the maximum entropy distributions according to generalized entropies. We show that at asymptotically large times and volumes, the scaling exponent of the anomalous diffusion process described by the generalized Fokker-Planck equation and the phase space volume scaling exponent of the generalized entropy bijectively determine each other via a simple algebraic relation. This implies that these basic measures characterizing the transient and the stationary behaviour of the processes provide the same information regarding the asymptotic regime, and consequently, the classification of the processes given by these two exponents coincide.

physics.gen-ph↗

arXiv2016

Comparing the hierarchy of keywords in on-line news portals

The tagging of on-line content with informative keywords is a widespread phenomenon from scientific article repositories through blogs to on-line news portals. In most of the cases, the tags on a given item are free words chosen by the authors independently. Therefore, relations among keywords in a collection of news items is unknown. However, in most cases the topics and concepts described by these keywords are forming a latent hierarchy, with the more general topics and categories at the top, and more specialised ones at the bottom. Here we apply a recent, cooccurrence-based tag hierarchy extraction method to sets of keywords obtained from four different on-line news portals. The resulting hierarchies show substantial differences not just in the topics rendered as important (being at the top of the hierarchy) or of less interest (categorised low in the hierarchy), but also in the underlying network structure. This reveals discrepancies between the plausible keyword association frameworks in the studied news portals.

physics.soc-ph↗

arXiv2016

Partial order similarity based on mutual information

Comparing the ranking of candidates by different voters is an important topic in social and information science with a high relevance from the point of view of practical applications. In general, ties and pairs of incomparable candidates may occur, thus, the alternative rankings are described by partial orders. Various distance measures between partial orders have already been introduced, where zero distance is corresponding to a perfect match between a pair of partial orders, and larger values signal greater differences. Here we take a different approach and propose a similarity measure based on adjusted mutual information. In general, the similarity value of unity is corresponding to exactly matching partial orders, while a low similarity is associated to a pair of independent partial orders. The time complexity of the computation of this similarity measure is $\mathcal{O}(\left|{\mathcal C}\right|^3)$ in the worst case, and $\mathcal{O}(\left|{\mathcal C}\right|^2\ln \left|{\mathcal C}\right|)$ in the typical case of partial orders corresponding to trees with constant branching number, where $\left|{\mathcal C}\right|$ denotes the number of candidates. An interesting feature of our approach is that the similarity measure is sensitive to the position of the disagreements in the ranking: Differences at the highly ranked candidates induce larger similarity drop compared to disagreements at the bottom candidates.

stat.AP↗

arXiv2015

Random walk hierarchy measure: What is more hierarchical, a chain, a tree or a star?

Signs of hierarchy are prevalent in a wide range of systems in nature and society. One of the key problems is quantifying the importance of hierarchical organisation in the structure of the network representing the interactions or connections between the fundamental units of the studied system. Although a number of notable methods are already available, their vast majority is treating all directed acyclic graphs as already maximally hierarchical. Here we propose a hierarchy measure based on random walks on the network. The novelty of our approach is that directed trees corresponding to multi level pyramidal structures obtain higher hierarchy scores compared to directed chains and directed stars. Furthermore, in the thermodynamic limit the hierarchy measure of regular trees is converging to a well defined limit depending only on the branching number. When applied to real networks, our method is computationally very effective, as the result can be evaluated with arbitrary precision by subsequent multiplications of the transition matrix describing the random walk process. In addition, the tests on real world networks provided very intuitive results, e.g., the trophic levels obtained from our approach on a food web were highly consistent with former results from ecology.

physics.soc-ph↗

arXiv2015

Hierarchical networks of scientific journals

Scientific journals are the repositories of the gradually accumulating knowledge of mankind about the world surrounding us. Just as our knowledge is organised into classes ranging from major disciplines, subjects and fields to increasingly specific topics, journals can also be categorised into groups using various metrics. In addition to the set of topics characteristic for a journal, they can also be ranked regarding their relevance from the point of overall influence. One widespread measure is impact factor, but in the present paper we intend to reconstruct a much more detailed description by studying the hierarchical relations between the journals based on citation data. We use a measure related to the notion of m-reaching centrality and find a network which shows the level of influence of a journal from the point of the direction and efficiency with which information spreads through the network. We can also obtain an alternative network using a suitably modified nested hierarchy extraction method applied to the same data. The results are weakly methodology-dependent and reveal non-trivial relations among journals. The two alternative hierarchies show large similarity with some striking differences, providing together a complex picture of the intricate relations between scientific journals.

physics.soc-ph↗

arXiv2015

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.

physics.soc-ph↗

arXiv2014

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.

cs.IR↗

arXiv2013

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.

physics.soc-ph↗

arXiv2012

Clustering of tag-induced sub-graphs in complex networks

We study the behavior of the clustering coefficient in tagged networks. The rich variety of tags associated with the nodes in the studied systems provide additional information about the entities represented by the nodes which can be important for practical applications like searching in the networks. Here we examine how the clustering coefficient changes when narrowing the network to a sub-graph marked by a given tag, and how does it correlate with various other properties of the sub-graph. Another interesting question addressed in the paper is how the clustering coefficient of the individual nodes is affected by the tags on the node. We believe these sort of analysis help acquiring a more complete description of the structure of large complex systems.

physics.soc-ph↗

arXiv2012

Parallel clustering with CFinder

The amount of available data about complex systems is increasing every year, measurements of larger and larger systems are collected and recorded. A natural representation of such data is given by networks, whose size is following the size of the original system. The current trend of multiple cores in computing infrastructures call for a parallel reimplementation of earlier methods. Here we present the grid version of CFinder, which can locate overlapping communities in directed, weighted or undirected networks based on the clique percolation method (CPM). We show that the computation of the communities can be distributed among several CPU-s or computers. Although switching to the parallel version not necessarily leads to gain in computing time, it definitely makes the community structure of extremely large networks accessible.

physics.soc-ph↗

arXiv2012

Ontologies and tag-statistics

Due to the increasing popularity of collaborative tagging systems, the research on tagged networks, hypergraphs, ontologies, folksonomies and other related concepts is becoming an important interdisciplinary topic with great actuality and relevance for practical applications. In most collaborative tagging systems the tagging by the users is completely "flat", while in some cases they are allowed to define a shallow hierarchy for their own tags. However, usually no overall hierarchical organisation of the tags is given, and one of the interesting challenges of this area is to provide an algorithm generating the ontology of the tags from the available data. In contrast, there are also other type of tagged networks available for research, where the tags are already organised into a directed acyclic graph (DAG), encapsulating the "is a sub-category of" type of hierarchy between each other. In this paper we study how this DAG affects the statistical distribution of tags on the nodes marked by the tags in various real networks. We analyse the relation between the tag-frequency and the position of the tag in the DAG in two large sub-networks of the English Wikipedia and a protein-protein interaction network. We also study the tag co-occurrence statistics by introducing a 2d tag-distance distribution preserving both the difference in the levels and the absolute distance in the DAG for the co-occurring pairs of tags. Our most interesting finding is that the local relevance of tags in the DAG, (i.e., their rank or significance as characterised by, e.g., the length of the branches starting from them) is much more important than their global distance from the root. Furthermore, we also introduce a simple tagging model based on random walks on the DAG, capable of reproducing the main statistical features of tag co-occurrence.

physics.soc-ph↗

arXiv2008

Fundamental statistical features and self-similar properties of tagged networks

We investigate the fundamental statistical features of tagged (or annotated) networks having a rich variety of attributes associated with their nodes. Tags (attributes, annotations, properties, features, etc.) provide essential information about the entity represented by a given node, thus, taking them into account represents a significant step towards a more complete description of the structure of large complex systems. Our main goal here is to uncover the relations between the statistical properties of the node tags and those of the graph topology. In order to better characterise the networks with tagged nodes, we introduce a number of new notions, including tag-assortativity (relating link probability to node similarity), and new quantities, such as node uniqueness (measuring how rarely the tags of a node occur in the network) and tag-assortativity exponent. We apply our approach to three large networks representing very different domains of complex systems. A number of the tag related quantities display analogous behaviour (e.g., the networks we studied are tag-assortative, indicating possible universal aspects of tags versus topology), while some other features, such as the distribution of the node uniqueness, show variability from network to network allowing for pin-pointing large scale specific features of real-world complex networks. We also find that for each network the topology and the tag distribution are scale invariant, and this self-similar property of the networks can be well characterised by the tag-assortativity exponent, which is specific to each system.

physics.soc-ph↗

arXiv2008

Centrality properties of directed module members in social networks

Several recent studies of complex networks have suggested algorithms for locating network communities, also called modules or clusters, which are mostly defined as groups of nodes with dense internal connections. Along with the rapid development of these clustering techniques, the ability of revealing overlaps between communities has become very important as well. An efficient search technique for locating overlapping modules is provided by the Clique Percolation Method (CPM) and its extension to directed graphs, the CPMd algorithm. Here we investigate the centrality properties of directed module members in social networks obtained from e-mail exchanges and from sociometric questionnaires. Our results indicate that nodes in the overlaps between modules play a central role in the studied systems. Furthermore, the two different types of networks show interesting differences in the relation between the centrality measures and the role of the nodes in the directed modules.

physics.soc-ph↗

arXiv2007

Directed network modules

A search technique locating network modules, i.e., internally densely connected groups of nodes in directed networks is introduced by extending the Clique Percolation Method originally proposed for undirected networks. After giving a suitable definition for directed modules we investigate their percolation transition in the Erdos-Renyi graph both analytically and numerically. We also analyse four real-world directed networks, including Google's own webpages, an email network, a word association graph and the transcriptional regulatory network of the yeast Saccharomyces cerevisiae. The obtained directed modules are validated by additional information available for the nodes. We find that directed modules of real-world graphs inherently overlap and the investigated networks can be classified into two major groups in terms of the overlaps between the modules. Accordingly, in the word-association network and among Google's webpages the overlaps are likely to contain in-hubs, whereas the modules in the email and transcriptional regulatory networks tend to overlap via out-hubs.

physics.soc-ph↗

arXiv2007

Quantifying social group evolution

The rich set of interactions between individuals in the society results in complex community structure, capturing highly connected circles of friends, families, or professional cliques in a social network. Thanks to frequent changes in the activity and communication patterns of individuals, the associated social and communication network is subject to constant evolution. Our knowledge of the mechanisms governing the underlying community dynamics is limited, but is essential for a deeper understanding of the development and self-optimisation of the society as a whole. We have developed a new algorithm based on clique percolation, that allows, for the first time, to investigate the time dependence of overlapping communities on a large scale and as such, to uncover basic relationships characterising community evolution. Our focus is on networks capturing the collaboration between scientists and the calls between mobile phone users. We find that large groups persist longer if they are capable of dynamically altering their membership, suggesting that an ability to change the composition results in better adaptability. The behaviour of small groups displays the opposite tendency, the condition for stability being that their composition remains unchanged. We also show that the knowledge of the time commitment of the members to a given community can be used for estimating the community's lifetime. These findings offer a new view on the fundamental differences between the dynamics of small groups and large institutions.

stat.ME↗