arXiv subjects

Guido Caldarelli

Publications and source records attributed to Guido Caldarelli.

At least 127 records · Page 7Linked to original sources

arXiv2008

Schroedinger-like PageRank equation and localization in the WWW

The WorldWide Web is one of the most important communication systems we use in our everyday life. Despite its central role, the growth and the development of the WWW is not controlled by any central authority. This situation has created a huge ensemble of connections whose complexity can be fruitfully described and quantified by network theory. One important application that allows to sort out the information present in these connections is given by the PageRank alghorithm. Computation of this quantity is usually made iteratively with a large use of computational time. In this paper we show that the PageRank can be expressed in terms of a wave function obeying a Schroedinger-like equation. In particular the topological disorder given by the unbalance of outgoing and ingoing links between pages, induces wave function and potential structuring. This allows to directly localize the pages with the largest score. Through this new representation we can now compute the PageRank without iterative techniques. For most of the cases of interest our method is faster than the original one. Our results also clarify the role of topology in the diffusion of information within complex networks. The whole approach opens the possibility to novel techniques inspired by quantum physics for the analysis of the WWW properties.

physics.soc-ph↗

arXiv2008

Barabasi Queueing Model and Invasion Percolation on a tree

In this paper we study the properties of the Barabási model of queueing under the hypothesis that the number of tasks is steadily growing in time. We map this model exactly onto an Invasion Percolation dynamics on a Cayley tree. This allows to recover the correct waiting time distribution $P_W(τ)\sim τ^{-3/2}$ at the stationary state (as observed in different realistic data) and also to characterize it as a sequence of causally and geometrically connected bursts of activity. We also find that the approach to stationarity is very slow.

physics.soc-ph↗

arXiv2008

Self-Organization and Complex Networks

In this chapter we discuss how the results developed within the theory of fractals and Self-Organized Criticality (SOC) can be fruitfully exploited as ingredients of adaptive network models. In order to maintain the presentation self-contained, we first review the basic ideas behind fractal theory and SOC. We then briefly review some results in the field of complex networks, and some of the models that have been proposed. Finally, we present a self-organized model recently proposed by Garlaschelli et al. [Nat. Phys. 3, 813 (2007)] that couples the fitness network model defined by Caldarelli et al. [Phys. Rev. Lett. 89, 258702 (2002)] with the evolution model proposed by Bak and Sneppen [Phys. Rev. Lett. 71, 4083 (1993)] as a prototype of SOC. Remarkably, we show that the results obtained for the two models separately change dramatically when they are coupled together. This indicates that self-organized networks may represent an entirely novel class of complex systems, whose properties cannot be straightforwardly understood in terms of what we have learnt so far.

cond-mat.dis-nn↗

arXiv2008

Self-organized network evolution coupled to extremal dynamics

The interplay between topology and dynamics in complex networks is a fundamental but widely unexplored problem. Here, we study this phenomenon on a prototype model in which the network is shaped by a dynamical variable. We couple the dynamics of the Bak-Sneppen evolution model with the rules of the so-called fitness network model for establishing the topology of a network; each vertex is assigned a fitness, and the vertex with minimum fitness and its neighbours are updated in each iteration. At the same time, the links between the updated vertices and all other vertices are drawn anew with a fitness-dependent connection probability. We show analytically and numerically that the system self-organizes to a non-trivial state that differs from what is obtained when the two processes are decoupled. A power-law decay of dynamical and topological quantities above a threshold emerges spontaneously, as well as a feedback between different dynamical regimes and the underlying correlation and percolation properties of the network.

cond-mat.stat-mech↗

arXiv2008

A Self-organized model for network evolution

Here we provide a detailed analysis, along with some extensions and additonal investigations, of a recently proposed self-organised model for the evolution of complex networks. Vertices of the network are characterised by a fitness variable evolving through an extremal dynamics process, as in the Bak-Sneppen model representing a prototype of Self-Organized Criticality. The network topology is in turn shaped by the fitness variable itself, as in the fitness network model. The system self-organizes to a nontrivial state, characterized by a power-law decay of dynamical and topological quantities above a critical threshold. The interplay between topology and dynamics in the system is the key ingredient leading to an unexpected behaviour of these quantities.

physics.soc-ph↗

arXiv2007

Folksonomies and clustering in the collaborative system CiteULike

We analyze CiteULike, an online collaborative tagging system where users bookmark and annotate scientific papers. Such a system can be naturally represented as a tripartite graph whose nodes represent papers, users and tags connected by individual tag assignments. The semantics of tags is studied here, in order to uncover the hidden relationships between tags. We find that the clustering coefficient reflects the semantical patterns among tags, providing useful ideas for the designing of more efficient methods of data classification and spam detection.

physics.soc-ph↗

arXiv2007

Uncovering the topology of configuration space networks

The configuration space network (CSN) of a dynamical system is an effective approach to represent the ensemble of configurations sampled during a simulation and their dynamic connectivity. To elucidate the connection between the CSN topology and the underlying free-energy landscape governing the system dynamics and thermodynamics, an analytical soluti on is provided to explain the heavy tail of the degree distribution, neighbor co nnectivity and clustering coefficient. This derivation allows to understand the universal CSN network topology observed in systems ranging from a simple quadratic well to the native state of the beta3s peptide and a 2D lattice heteropolymer. Moreover CSN are shown to fall in the general class of complex networks describe d by the fitness model.

cond-mat.stat-mech↗

arXiv2007

Critical transient in the Barabási model of human dynamics

We introduce an exact probabilistic description for L=2 of the Barabási model for the dynamics of a list of L tasks. This permits to study the problem out of stationarity, and to solve explicitly the extremal limit case where a critical behavior for the waiting time distribution is observed. This behavior deviates at any finite time from that of the stationary state. We study also the characteristic relaxation time for finite time deviations from stationarity in all cases showing that it diverges in the extremal limit confirming that this deviations are important at all time.

physics.soc-ph↗

arXiv2006

Trading strategies in the Italian interbank market

Using a data set which includes all transactions among banks in the Italian money market, we study their trading strategies and the dependence among them. We use the Fourier method to compute the variance-covariance matrix of trading strategies. Our results indicate that well defined patterns arise. Two main communities of banks, which can be coarsely identified as small and large banks, emerge.

physics.soc-ph↗

arXiv2005

Loops structure of the Internet at the Autonomous System Level

We present here a study of the clustering and cycles in the graph of Internet at the Autonomous Systems level. We show that,even if the whole structure is changing with time, the statistical distributions of loops of order 3,4,5 remain stable during the evolution. Moreover we will bring evidence that the Internet graphs show characteristic Markovian signatures, since the loops structure is very well described by the two point correlations between the connectivities of the nodes. This represent another essential characteristic of this evolving graph. To capture this feature of the Internet represent one of the challenges in the future Internet modeling.

cond-mat.dis-nn↗

arXiv2005

Spectral methods cluster words of the same class in a syntactic dependency network

We analyze here a particular kind of linguistic network where vertices representwords and edges stand for syntactic relationships between words. The statisticalproperties of these networks have been recently studied and various features such as the small-world phenomenon and a scale-free distribution of degrees have been found. Our work focuses on four classes of words: verbs, nouns, adverbs and adjectives. Here, we use spectral methods sorting vertices. We show that the ordering clusters words of the same class. For nouns and verbs, the cluster size distribution clearly follows a power-law distribution that cannot be explained by a null hypothesis. Long-range correlations are found between vertices in theordering provided by the spectral method. The findings support the use of spectral methods for detecting community structure.

cond-mat.stat-mech↗

arXiv2004

The scale-free topology of market investments

We propose a network description of large market investments, where both stocks and shareholders are represented as vertices connected by weighted links corresponding to shareholdings. In this framework, the in-degree ($k_{in}$) and the sum of incoming link weights ($v$) of an investor correspond to the number of assets held (\emph{portfolio diversification}) and to the invested wealth (\emph{portfolio volume}) respectively. An empirical analysis of three different real markets reveals that the distributions of both $k_{in}$ and $v$ display power-law tails with exponents $γ$ and $α$. Moreover, we find that $k_{in}$ scales as a power-law function of $v$ with an exponent $β$. Remarkably, despite the values of $α$, $β$ and $γ$ differ across the three markets, they are always governed by the scaling relation $β=(1-α)/(1-γ)$. We show that these empirical findings can be reproduced by a recent model relating the emergence of scale-free networks to an underlying Paretian distribution of `hidden' vertex properties.

cond-mat.stat-mech↗

arXiv2004

Detecting communities in large networks

We develop an algorithm to detect community structure in complex networks. The algorithm is based on spectral methods and takes into account weights and links orientations. Since the method detects efficiently clustered nodes in large networks even when these are not sharply partitioned, it turns to be specially suitable to the analysis of social and information networks. We test the algorithm on a large-scale data-set from a psychological experiment of word association. In this case, it proves to be successful both in clustering words and in uncovering mental association patterns.

cond-mat.dis-nn↗

arXiv2003

Preferential Exchange: Strengthening Connections in Complex Networks

Many social, technological and biological interactions involve network relationships whose outcome intimately depends on the structure of the network and on the strengths of the connections. Yet, although much information is now available concerning the structure of many networks, the strengths are more difficult to measure. Here we show that, for one particular social network, notably the e-mail network, a suitable measure of the strength of the connections can be available. We also propose a simple mechanism, based on positive feedback and reciprocity, that can explain the observed behavior and that hints toward specific dynamics of formation and reinforcement of network connections. Network data from contexts different from social sciences indicate that power-law, and generally broad, distributions of the connection strength are ubiquitous, and the proposed mechanism has a wide range of applicability.

cond-mat.stat-mech↗

arXiv2003

On the Widespread Occurrence of the Inverse Square Distribution in Social Sciences and Taxonomy

The widespread occurrence of an inverse square relation in the hierarchical distribution of sub-communities within communities (or sub-species within species) has been recently invoked as a signature of hierarchical self-organization within social and ecological systems. Here we show that, whether such systems are self-organized or not, this behavior is the consequence of the tree-like classification method. Different tree-like classifications (both of real and truly random systems) display a similar statistical behaviour when considering the sizes of their sub-branches.

cond-mat.stat-mech↗

arXiv2003

Number of h-cycles in the Internet at the Autonomous Systems level

We present here a study of the clustering and cycles present in the graph of Internet at the Autonomous Systems level. Even if the whole structure is changing with time, we present some evidence that the statistical distributions of cycles of order 3,4,5 remain stable during the evolution. This could suggest that cycles are among the characteristic motifs of the Internet. Furthermore, we compare data with the results obtained for growing network models aimed to reproduce the Internet evolution. Namely the fitness model and the Generalized Network Growth model. We are able to find some qualitative agreement with the experimental situation even if the actual number of loops seems to be larger in the data than in any proposed growing network models. The task to capture this feature of the Internet represent one of the challenges in the future Internet modeling.

cond-mat.dis-nn↗

arXiv2003

Vertex Intrinsic Fitness: How to Produce Arbitrary Scale-Free Networks

We study a recent model of random networks based on the presence of an intrinsic character of the vertices called fitness. The vertices fitnesses are drawn from a given probability distribution density. The edges between pair of vertices are drawn according to a linking probability function depending on the fitnesses of the two vertices involved. We study here different choices for the probability distribution densities and the linking functions. We find that, irrespective of the particular choices, the generation of scale-free networks is straightforward. We then derive the general conditions under which scale-free behavior appears. This model could then represent a possible explanation for the ubiquity and robustness of such structures.

cond-mat.stat-mech↗

arXiv2003

Assortative model for social networks

In this paper we present a new version of a network growth model, generalized in order to describe the behavior of social networks. The case of study considered is the preprint archive at cul.arxiv.org. Each node corresponds to a scientist, and a link is present whenever two authors wrote a paper together. This graph is a nice example of degree-assortative network, that is to say a network where sites with similar degree are connected each other. The model presented is one of the few able to reproduce such behavior, giving some insight on the microscopic dynamics at the basis of the graph structure.

cond-mat↗