Taxonomy and clustering in collaborative systems: the case of the on-line encyclopedia Wikipedia

In this paper we investigate the nature and structure of the relation between imposed classifications and real clustering in a particular case of a scale-free network given by the on-line encyclopedia Wikipedia. We find a statistical similarity in the distributions of community sizes both by using the top-down approach of the categories division present in the archive and in the bottom-up procedure of community detection given by an algorithm based on the spectral properties of the graph. Regardless the statistically similar behaviour the two methods provide a rather different division of the articles, thereby signaling that the nature and presence of power laws is a general feature for these systems and cannot be used as a benchmark to evaluate the suitability of a clustering method.Comment: 5 pages, 3 figures, epl2 styl

Beauty and Distance in the Stable Marriage Problem

The stable marriage problem has been introduced in order to describe a complex system where individuals attempt to optimise their own satisfaction, subject to mutually conflicting constraints. Due to the potential large applicability of such model to describe all the situation where different objects has to be matched pairwise, the statistical properties of this model have been extensively studied. In this paper we present a generalization of this model, introduced in order to take into account the presence of correlations in the lists and the effects of distance when the player are supposed to be represented by a position in space.Comment: 8 pages, 3 figures, submitted to ep

Quantitative description and modeling of real networks

In this letter we present data analysis and modeling of two particular cases of study in the field of growing networks. We analyze WWW data set and authorship collaboration networks in order to check the presence of correlation in the data. The results are reproduced with a pretty good agreement through a suitable modification of the standard AB model of network growth. In particular, intrinsic relevance of sites plays a role in determining the future degree of the vertex.Comment: 4 pages, 3 figure

Preferential attachment in the growth of social networks: the case of Wikipedia

We present an analysis of the statistical properties and growth of the free on-line encyclopedia Wikipedia. By describing topics by vertices and hyperlinks between them as edges, we can represent this encyclopedia as a directed graph. The topological properties of this graph are in close analogy with that of the World Wide Web, despite the very different growth mechanism. In particular we measure a scale--invariant distribution of the in-- and out-- degree and we are able to reproduce these features by means of a simple statistical model. As a major consequence, Wikipedia growth can be described by local rules such as the preferential attachment mechanism, though users can act globally on the network.Comment: 4 pages, 4 figures, revte

A Yule-Simon process with memory

The Yule-Simon model has been used as a tool to describe the growth of diverse systems, acquiring a paradigmatic character in many fields of research. Here we study a modified Yule-Simon model that takes into account the full history of the system by means of an hyperbolic memory kernel. We show how the memory kernel changes the properties of preferential attachment and provide an approximate analytical solution for the frequency distribution density as well as for the frequency-rank distribution.Comment: 7 pages, 5 figures; accepted for publication in Europhysics Letter

The Conformal Penrose Limit and the Resolution of the pp-curvature Singularities

We consider the exact solutions of the supergravity theories in various dimensions in which the space-time has the form M_{d} x S^{D-d} where M_{d} is an Einstein space admitting a conformal Killing vector and S^{D-d} is a sphere of an appropriate dimension. We show that, if the cosmological constant of M_{d} is negative and the conformal Killing vector is space-like, then such solutions will have a conformal Penrose limit: M^{(0)}_{d} x S^{D-d} where M^{(0)}_{d} is a generalized d-dimensional AdS plane wave. We study the properties of the limiting solutions and find that M^{(0)}_{d} has 1/4 supersymmetry as well as a Virasoro symmetry. We also describe how the pp-curvature singularity of M^{(0)}_{d} is resolved in the particular case of the D6-branes of D=10 type IIA supergravity theory. This distinguished case provides an interesting generalization of the plane waves in D=11 supergravity theory and suggests a duality between the SU(2) gauged d=8 supergravity of Salam and Sezgin on M^{(0)}_{8} and the d=7 ungauged supergravity theory on its pp-wave boundary.Comment: 20 pages, LaTeX; typos corrected, journal versio