arXiv subjects

Santo Fortunato

Publications and source records attributed to Santo Fortunato.

At least 109 records · Page 6Linked to original sources

arXiv2006

Decoding the structure of the WWW: facts versus sampling biases

The understanding of the immense and intricate topological structure of the World Wide Web (WWW) is a major scientific and technological challenge. This has been tackled recently by characterizing the properties of its representative graphs in which vertices and directed edges are identified with web-pages and hyperlinks, respectively. Data gathered in large scale crawls have been analyzed by several groups resulting in a general picture of the WWW that encompasses many of the complex properties typical of rapidly evolving networks. In this paper, we report a detailed statistical analysis of the topological properties of four different WWW graphs obtained with different crawlers. We find that, despite the very large size of the samples, the statistical measures characterizing these graphs differ quantitatively, and in some cases qualitatively, depending on the domain analyzed and the crawl used for gathering the data. This spurs the issue of the presence of sampling biases and structural differences of Web crawls that might induce properties not representative of the actual global underlying graph. In order to provide a more accurate characterization of the Web graph and identify observables which are clearly discriminating with respect to the sampling process, we study the behavior of degree-degree correlation functions and the statistics of reciprocal connections. The latter appears to enclose the relevant correlations of the WWW graph and carry most of the topological information of theWeb. The analysis of this quantity is also of major interest in relation to the navigability and searchability of the Web.

cs.NI↗

arXiv2005

How to make the top ten: Approximating PageRank from in-degree

PageRank has become a key element in the success of search engines, allowing to rank the most important hits in the top screen of results. One key aspect that distinguishes PageRank from other prestige measures such as in-degree is its global nature. From the information provider perspective, this makes it difficult or impossible to predict how their pages will be ranked. Consequently a market has emerged for the optimization of search engine results. Here we study the accuracy with which PageRank can be approximated by in-degree, a local measure made freely available by search engines. Theoretical and empirical analyses lead to conclude that given the weak degree correlations in the Web link graph, the approximation can be relatively accurate, giving service and information providers an effective new marketing tool.

cs.IR↗

arXiv2005

Vector Opinion Dynamics in a Bounded Confidence Consensus Model

We study the continuum opinion dynamics of the compromise model of Krause and Hegselmann for a community of mutually interacting agents, by solving numerically a rate equation. The opinions are here represented by bidimensional vectors with real-valued components. We study the situation starting from a uniform probability distribution for the opinion configuration and for different shapes of the confidence range. In all cases, we find that the thresholds for consensus and cluster merging either coincide with their one-dimensional counterparts, or are very close to them. The symmetry of the final opinion configuration, when more clusters survive, is determined by the shape of the opinion space. If the latter is a square, which is the case we consider, the clusters in general occupy the sites of a square lattice, although we sometimes observe interesting deviations from this general pattern, especially near the center of the opinion space.

physics.soc-ph↗

arXiv2005

Computer Simulations of Opinions

We review the opinion dynamics in the computer models of Deffuant et al. (D), of Krause and Hegselmann (KH), and of Sznajd (S). All these models allow for consensus (one final opinion), polarization (two final opinions), and fragmentation (more than two final opinions), depending on how tolerant people are to different opinions. We then simulate the reactions of people to ex treme events, in that we modify the opinion of an individual and investigate how the dynamics of a consensus model diffuses this perturbation among the other members of a community. It often happens that the original shock induced by the extreme event influences the opinion of a big part of the society.

cond-mat.dis-nn↗

arXiv2005

Monte Carlo Simulations of Opinion Dynamics

We briefly introduce a new promising field of applications of statistical physics, opinion dynamics, where the systems at study are social groups or communities and the atoms/spins are the individuals (or agents) belonging to such groups. The opinion of each agent is modeled by a number, integer or real, and simple rules determine how the opinions vary as a consequence of discussions between people. Monte Carlo simulations of consensus models lead to patterns of self-organization among the agents which fairly well reproduce the trends observed in real social systems.

cond-mat.stat-mech↗

arXiv2004

Number of spanning clusters at the high-dimensional percolation thresholds

A scaling theory is used to derive the dependence of the average number of spanning clusters at threshold on the lattice size L. This number should become independent of L for dimensions d<6, and vary as log L at d=6. The predictions for d>6 depend on the boundary conditions, and the results there may vary between L^{d-6} and L^0. While simulations in six dimensions are consistent with this prediction (after including corrections of order loglog L), in five dimensions the average number of spanning clusters still increases as log L even up to L = 201. However, the histogram P(k) of the spanning cluster multiplicity does scale as a function of kX(L), with X(L)=1+const/L, indicating that for sufficiently large L the average will approach a finite value: a fit of the 5D multiplicity data with a constant plus a simple linear correction to scaling reproduces the data very well. Numerical simulations for d>6 and for d=4 are also presented.

cond-mat.stat-mech↗

arXiv2004

On the Consensus Threshold for the Opinion Dynamics of Krause-Hegselmann

In the consensus model of Krause-Hegselmann, opinions are real numbers between 0 and 1 and two agents are compatible if the difference of their opinions is smaller than the confidence bound parameter ε. A randomly chosen agent takes the average of the opinions of all neighbouring agents which are compatible with it. We propose a conjecture, based on numerical evidence, on the value of the consensus threshold ε_c of this model. We claim that ε_c can take only two possible values, depending on the behaviour of the average degree d of the graph representing the social relationships, when the population N goes to infinity: if d diverges when N goes to infinity, ε_c equals the consensus threshold ε_i ~ 0.2 on the complete graph; if instead d stays finite when N goes to infinity, ε_c=1/2 as for the model of Deffuant et al.

cond-mat.stat-mech↗

arXiv2004

A Method to Find Community Structures Based on Information Centrality

Community structures are an important feature of many social, biological and technological networks. Here we study a variation on the method for detecting such communities proposed by Girvan and Newman and based on the idea of using centrality measures to define the community boundaries (M. Girvan and M. E. J. Newman, Community structure in social and biological networks Proc. Natl. Acad. Sci. USA 99, 7821-7826 (2002)). We develop an algorithm of hierarchical clustering that consists in finding and removing iteratively the edge with the highest information centrality. We test the algorithm on computer generated and real-world networks whose community structure is already known or has been studied by means of other methods. We show that our algorithm, although it runs to completion in a time O(n^4), is very effective especially when the communities are very mixed and hardly detectable by the other methods.

cond-mat.stat-mech↗

arXiv2004

Do extremists impose the structure of social networks?

The structure and the properties of complex networks essentially depend on the way how nodes get connected to each other. We assume here that each node has a feature which attracts the others. We model the situation by assigning two numbers to each node, ωand α, where ωindicates some property of the node and αthe affinity towards that property. A node A is more likely to establish a connection with a node B if B has a high value of ωand A has a high value of α. Simple computer simulations show that networks built according to this principle have a degree distribution with a power law tail, whose exponent is determined only by the nodes with the largest value of the affinity α(the "extremists"). This means that the extremists lead the formation process of the network and manage to shape the final topology of the system. The latter phenomenon may have implications in the study of social networks and in epidemiology.

cond-mat.stat-mech↗

arXiv2004

The Sznajd Consensus Model with Continuous Opinions

In the consensus model of Sznajd, opinions are integers and a randomly chosen pair of neighbouring agents with the same opinion forces all their neighbours to share that opinion. We propose a simple extension of the model to continuous opinions, based on the criterion of bounded confidence which is at the basis of other popular consensus models. Here the opinion s is a real number between 0 and 1, and a parameter εis introduced such that two agents are compatible if their opinions differ from each other by less than ε. If two neighbouring agents are compatible, they take the mean s_m of their opinions and try to impose this value to their neighbours. We find that if all neighbours take the average opinion s_m the system reaches complete consensus for any value of the confidence bound ε. We propose as well a weaker prescription for the dynamics and discuss the corresponding results.

cond-mat.stat-mech↗

arXiv2004

Universality of the Threshold for Complete Consensus for the Opinion Dynamics of Deffuant et al

In the compromise model of Deffuant et al., opinions are real numbers between 0 and 1 and two agents are compatible if the difference of their opinions is smaller than the confidence bound parameter ε. The opinions of a randomly chosen pair of compatible agents get closer to each other. We provide strong numerical evidence that the threshold value of εabove which all agents share the same opinion in the final configuration is 1/2, independently of the underlying social topology.

cond-mat.stat-mech↗

arXiv2004

Damage Spreading and Opinion Dynamics on Scale Free Networks

We study damage spreading among the opinions of a system of agents, subjected to the dynamics of the Krause-Hegselmann consensus model. The damage consists in a sharp change of the opinion of one or more agents in the initial random opinion configuration, supposedly due to some external factors and/or events. This may help to understand for instance under which conditions special shocking events or targeted propaganda are able to influence the results of elections. For agents lying on the nodes of a Barabasi-Albert network, there is a damage spreading transition at a low value epsilon_d of the confidence bound parameter. Interestingly, we find as well that there is some critical value epsilon_s above which the initial perturbation manages to propagate to all other agents.

cond-mat.stat-mech↗

arXiv2004

The Krause-Hegselmann Consensus Model with Discrete Opinions

The consensus model of Krause and Hegselmann can be naturally extended to the case in which opinions are integer instead of real numbers. Our algorithm is much faster than the original version and thus more suitable for applications. For the case of a society in which everybody can talk to everybody else, we find that the chance to reach consensus is much higher as compared to other models; if the number of possible opinions Q<=7, in fact, consensus is always reached, which might explain the stability of political coalitions with more than three or four parties. For Q>7 the number S of surviving opinions is approximately the same independently of the size N of the population, as long as Q<N. We considered as well the more realistic case of a society structured like a Barabasi-Albert network; here the consensus threshold depends on the outdegree of the nodes and we find a simple scaling law for S, as observed for the discretized Deffuant model.

cond-mat.stat-mech↗

arXiv2004

The Hagedorn Temperature and Partition Thermodynamics

We review the resonance gas formalism of hadron thermodynamics and recall that an exponential increase of the resonance spectrum leads to a limiting temperature of hadronic matter. We then show that the number p(n) of ordered partitions of an integer n grows exponentially with n and satisfies the integer counterpart of the statistical bootstrap equation. Considering the set of all partitions as a Gibbs ensemble provides a partition thermodynamics which is also governed by a limiting temperature, determined by the combinatorial structure of the problem. Further associating intrinsic quantum numbers to integers results in a phase diagram equivalent to that found in QCD for hadronic matter as function of temperature and baryochemical potential.

hep-ph↗

arXiv2002

Cluster Percolation and Critical Behaviour in Spin Models and SU(N) Gauge Theories

The critical behaviour of several spin models can be simply described as percolation of some suitably defined clusters, or droplets: the onset of the geometrical transition coincides with the critical point and the percolation exponents are equal to the thermal exponents. It is still unknown whether, given a model, one can define at all the droplets. In the cases where this is possible, the droplet definition depends in general on the specific model at study and can be quite involved. We propose here a simple general definition for the droplets: they are clusters obtained by joining nearest-neighbour spins of the same sign with some bond probability p_B, which is the minimal probability that still allows the existence of a percolating cluster at the critical temperature T_c. By means of lattice Monte Carlo simulations we find that this definition indeed satisfies the conditions required for the droplets, for many classical spin models, discrete and continuous, both in two and in three dimensions. In particular, our prescription allows to describe exactly the confinement-deconfinement transition of SU(N) gauge theories as Polyakov loop percolation.

hep-lat↗

arXiv2002

Site Percolation and Phase Transitions in Two Dimensions

The properties of the pure-site clusters of spin models, i.e. the clusters which are obtained by joining nearest-neighbour spins of the same sign, are here investigated. In the Ising model in two dimensions it is known that such clusters undergo a percolation transition exactly at the critical point. We show that this result is valid for a wide class of bidimensional systems undergoing a continuous magnetization transition. We provide numerical evidence for discrete as well as for continuous spin models, including SU(N) lattice gauge theories. The critical percolation exponents do not coincide with the ones of the thermal transition, but they are the same for models belonging to the same universality class.

cond-mat.stat-mech↗

arXiv2001

Euler-Poincare' Characteristic and Phase Transition in the Potts Model

Recent results concerning the topological properties of random geometrical sets have been successfully applied to the study of the morphology of clusters in percolation theory. This approach provides an alternative way of inspecting the critical behaviour of random systems in statistical mechanics. For the 2d q-states Potts model with q <= 6, intensive and accurate numerics indicates that the average of the Euler characteristic (taken with respect to the Fortuin-Kasteleyn random cluster measure) is an order parameter of the phase transition.

cond-mat.stat-mech↗

arXiv2001

Cluster Percolation and Explicit Symmetry Breaking in Spin Models

Many features of spin models can be interpreted in geometrical terms by means of the properties of well defined clusters of spins. In case of spontaneous symmetry breaking, the phase transition of models like the q-state Potts model, O(n), etc., can be equivalently described as a percolation transition of clusters. We study here the behaviour of such clusters when the presence of an external field H breaks explicitly the global symmetry of the Hamiltonian of the theory. We find that these clusters have still some interesting relationships with thermal features of the model.

hep-lat↗