Péter Pollner

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 Erdős–Renyi graph both analytically and numerically. We also analyse four real-world directed networks, including Googles own web-pages, 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 Googles web-pages, overlaps are likely to contain in-hubs, whereas the modules in the email and transcriptional regulatory network tend to overlap via out-hubs.

Preferential attachment of communities: The same principle, but a higher level

The graph of communities is a network emerging above the level of individual nodes in the hierarchical organisation of a complex system. In this graph the nodes correspond to communities (highly interconnected subgraphs, also called modules or clusters), and the links refer to members shared by two communities. Our analysis indicates that the development of this modular structure is driven by preferential attachment, in complete analogy with the growth of the underlying network of nodes. We study how the links between communities are born in a growing co-authorship network, and introduce a simple model for the dynamics of overlapping communities.

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 characterize 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 characterized by the tag-assortativity exponent, which is specific to each system.

Social Group Dynamics in Networks

The rich set of interactions between individuals in the society results in complex community structure, capturing highly connected circles of friends, fam- ilies, or professional cliques in a social network. Due to the frequent changes in the activity and communication patterns of individuals, the associated social and communication network is subject to constant evolution. The cohesive groups of people in such networks can grow by recruiting new members, or contract by loos- ing members; two (or more) groups may merge into a single community, while a large enough social group can split into several smaller ones; new communities are born and old ones may disappear. We discuss a new algorithm based on a clique percolation technique, that allows to investigate in detail the time dependence of communities on a large scale and as such, to uncover basic relationships of the sta- tistical features of community evolution. According to the results, the behaviour of smaller collaborative or friendship circles and larger communities, e.g., institutions show significant differences. Social groups containing only a few members persist longer on average when the fluctuations of the members is small. In contrast, we find that the condition for stability for large communities is continuous changes in their membership, allowing for the possibility that after some time practically all members are exchanged.

k-Clique Percolation and Clustering

We summarise recent results connected to the concept of k-clique percolation. This approach can be considered as a generalisation of edge percolation with a great potential as a community finding method in real-world graphs. We present a detailed study of the critical point for the appearance of a giant k-clique percolation cluster in the Erdős-Renyi-graph. The observed transition is continuous and at the transition point the scaling of the giant component with the number of vertices is highly non-trivial. The concept is extended to weighted and directed graphs as well. Finally, we demonstrate the effectiveness of k-clique percolation as a community finding method via a series of real-world applications.

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.

New method for computing topological pressure.

The topological pressure introduced by Ruelle and similar quantities describe dynamical multifractal properties of dynamical systems. These are important characteristics of mesoscopic systems in the classical regime. Original definition of these quantities are based on the symbolic description of the dynamics. It is hard or impossible to find symbolic description and generating partition to a general dynamical system, therefore these quantities are often not accessible for further studies. Here we present a new method by which the symbolic description can be omitted. We apply the method for a mixing and an intermittent system.

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.

Rotated multifractal network generator

The recently introduced multifractal network generator (MFNG), has been shown to provide a simple and flexible tool for creating random graphs with very diverse features. The MFNG is based on multifractal measures embedded in 2d, leading also to isolated nodes, whose number is relatively low for realistic cases, but may become dominant in the limiting case of infinitely large network sizes. Here we discuss the relation between this effect and the information dimension for the 1d projection of the link probability measure (LPM), and argue that the node isolation can be avoided by a simple transformation of the LPM based on rotation.

A nationwide study of the epidemiology of relapsing polychondritis

Objective Relapsing polychondritis (RP) is a rare autoimmune inflammatory disease that attacks mainly cartilaginous structures or causes serious damage in proteoglycan-rich structures (the eyes, heart, blood vessels, inner ear). This study shows results regarding the epidemiology, progression, and associations of this highly variable disease by collecting all cases from a 124-million-person-year Central European nationwide cohort. Methods We used the Hungarian Health Care Database to identify all persons with possible RP infection. We followed patients who had International Classification of Diseases 10th edition code M94.1 at least once in their inpatient or outpatient records between January 1, 2002 and December 31, 2013 in Hungary. We classified these patients into disease severity groups by their drug consumption patterns between January 1, 2010 and December 31, 2013. We analyzed the regional distribution of RP incidences as well. Overall maps of comorbidity are presented with network layouts. Results We identified 256 patients with RP among cumulatively 11.5 million registered inhabitants. We classified these patients into four severity classes as “extremely mild” (n=144), “mild” (n=22), “moderate” (n=41), and “severe” (n=4). Two additional groups were defined for patients without available drug data as “suspected only” (n=23) and “confirmed but unknown treatment” (n=22). The age and sex distributions of patients were similar to worldwide statistics. Indeed, the overall survival was good (95% confidence interval for 5 years was 83.6%–92.9% and for 10 years was 75.0%–88.3% which corresponds to the overall survival of the general population in Hungary), and the associations with other autoimmune disorders were high (56%) in Hungary. Almost any disease can occur with RP; however, the symptoms of chromosomal abnormalities are only incidental. Spondylosis can be a sign of the activation of RP, while Sjögren syndrome is the most frequent autoimmune association. Regional distribution of incidences suggests arsenic drinking water and sunlight exposure as possible triggering factors. Conclusion The good survival rate of RP in Hungary is probably associated with the early diagnosis of the disease.