222 research outputs found
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
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