Scientometrics: Untangling the topics

Measuring science is based on comparing articles to similar others. However, keyword-based groups of thematically similar articles are dominantly small. These small sizes keep the statistical errors of comparisons high. With the growing availability of bibliographic data such statistical errors can be reduced by merging methods of thematic grouping, citation networks and keyword co-usage.Comment: 2 pages, 2 figure

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.Comment: 21 pages, 10 figures, version 2: added two paragaph

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.Comment: 7 pages, 3 figure

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.Comment: Accepted for publication in JSTA

A 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.Comment: 8 pages LaTeX with revtex.sty, the 4 postscript figures are included using psfig.tex to appear in PR

Community structure and ethnic preferences in school friendship networks

Recently developed concepts and techniques of analyzing complex systems provide new insight into the structure of social networks. Uncovering recurrent preferences and organizational principles in such networks is a key issue to characterize them. We investigate school friendship networks from the Add Health database. Applying threshold analysis, we find that the friendship networks do not form a single connected component through mutual strong nominations within a school, while under weaker conditions such interconnectedness is present. We extract the networks of overlapping communities at the schools (c-networks) and find that they are scale free and disassortative in contrast to the direct friendship networks, which have an exponential degree distribution and are assortative. Based on the network analysis we study the ethnic preferences in friendship selection. The clique percolation method we use reveals that when in minority, the students tend to build more densely interconnected groups of friends. We also find an asymmetry in the behavior of black minorities in a white majority as compared to that of white minorities in a black majority.Comment: submitted to Physica

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

Spectral correlations in systems undergoing a transition from periodicity to disorder

We study the spectral statistics for extended yet finite quasi 1-d systems which undergo a transition from periodicity to disorder. In particular we compute the spectral two-point form factor, and the resulting expression depends on the degree of disorder. It interpolates smoothly between the two extreme limits -- the approach to Poissonian statistics in the (weakly) disordered case, and the universal expressions derived for the periodic case. The theoretical results agree very well with the spectral statistics obtained numerically for chains of chaotic billiards and graphs.Comment: 16 pages, Late