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

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

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

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

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