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

Number of loops of size h in growing scale-free networks

The hierarchical structure of scale-free networks has been investigated focusing on the scaling of the number $N_h(t)$ of loops of size h as a function of the system size. In particular we have found the analytic expression for the scaling of $N_h(t)$ in the Barab\'asi-Albert (BA) scale-free network. We have performed numerical simulations on the scaling law for $N_h(t)$ in the BA network and in other growing scale free networks, such as the bosonic network (BN) and the aging nodes (AN) network. We show that in the bosonic network and in the aging node network the phase transitions in the topology of the network are accompained by a change in the scaling of the number of loops with the system size.Comment: 4 pages, 3 figure

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

Finding instabilities in the community structure of complex networks

The problem of finding clusters in complex networks has been extensively studied by mathematicians, computer scientists and, more recently, by physicists. Many of the existing algorithms partition a network into clear clusters, without overlap. We here introduce a method to identify the nodes lying ``between clusters'' and that allows for a general measure of the stability of the clusters. This is done by adding noise over the weights of the edges of the network. Our method can in principle be applied with any clustering algorithm, provided that it works on weighted networks. We present several applications on real-world networks using the Markov Clustering Algorithm (MCL).Comment: 4 pages, 5 figure

Computation of the conformal algebra of 1+3 decomposable spacetimes

The conformal algebra of a 1+3 decomposable spacetime can be computed from the conformal Killing vectors (CKV) of the 3-space. It is shown that the general form of such a 3-CKV is the sum of a gradient CKV and a Killing or homothetic 3-vector. It is proved that spaces of constant curvature always admit such conformal Killing vectors. As an example, the complete conformal algebra of a G\"odel-type spacetime is computed. Finally it is shown that this method can be extended to compute the conformal algebra of more general non-decomposable spacetimes.Comment: 15 pages Latex, no figures. Minor mistakes correcte

Community Aliveness: Discovering Interaction Decay Patterns in Online Social Communities

Online Social Communities (OSCs) provide a medium for connecting people, sharing news, eliciting information, and finding jobs, among others. The dynamics of the interaction among the members of OSCs is not always growth dynamics. Instead, a $\textit{decay}$ or $\textit{inactivity}$ dynamics often happens, which makes an OSC obsolete. Understanding the behavior and the characteristics of the members of an inactive community help to sustain the growth dynamics of these communities and, possibly, prevents them from being out of service. In this work, we provide two prediction models for predicting the interaction decay of community members, namely: a Simple Threshold Model (STM) and a supervised machine learning classification framework. We conducted evaluation experiments for our prediction models supported by a $\textit{ground truth}$ of decayed communities extracted from the StackExchange platform. The results of the experiments revealed that it is possible, with satisfactory prediction performance in terms of the F1-score and the accuracy, to predict the decay of the activity of the members of these communities using network-based attributes and network-exogenous attributes of the members. The upper bound of the prediction performance of the methods we used is $0.91$ and $0.83$ for the F1-score and the accuracy, respectively. These results indicate that network-based attributes are correlated with the activity of the members and that we can find decay patterns in terms of these attributes. The results also showed that the structure of the decayed communities can be used to support the alive communities by discovering inactive members.Comment: pre-print for the 4th European Network Intelligence Conference - 11-12 September 2017 Duisburg, German