arXiv subjects

Filippo Radicchi

Publications and source records attributed to Filippo Radicchi.

At least 109 records · Page 6Linked to original sources

arXiv2011

Who is the best player ever? A complex network analysis of the history of professional tennis

We consider all matches played by professional tennis players between 1968 and 2010, and, on the basis of this data set, construct a directed and weighted network of contacts. The resulting graph shows complex features, typical of many real networked systems studied in literature. We develop a diffusion algorithm and apply it to the tennis contact network in order to rank professional players. Jimmy Connors is identified as the best player of the history of tennis according to our ranking procedure. We perform a complete analysis by determining the best players on specific playing surfaces as well as the best ones in each of the years covered by the data set. The results of our technique are compared to those of two other well established methods. In general, we observe that our ranking method performs better: it has a higher predictive power and does not require the arbitrary introduction of external criteria for the correct assessment of the quality of players. The present work provides a novel evidence of the utility of tools and methods of network theory in real applications.

physics.soc-ph↗

arXiv2011

Explosive percolation in graphs

Percolation is perhaps the simplest example of a process exhibiting a phase transition and one of the most studied phenomena in statistical physics. The percolation transition is continuous if sites/bonds are occupied independently with the same probability. However, alternative rules for the occupation of sites/bonds might affect the order of the transition. A recent set of rules proposed by Achlioptas et al. [Science 323, 1453 (2009)], characterized by competitive link addition, was claimed to lead to a discontinuous connectedness transition, named "explosive percolation". In this work we survey a numerical study of the explosive percolation transition on various types of graphs, from lattices to scale-free networks, and show the consistency of these results with recent analytical work showing that the transition is actually continuous.

cond-mat.stat-mech↗

arXiv2010

Combinatorial approach to Modularity

Communities are clusters of nodes with a higher than average density of internal connections. Their detection is of great relevance to better understand the structure and hierarchies present in a network. Modularity has become a standard tool in the area of community detection, providing at the same time a way to evaluate partitions and, by maximizing it, a method to find communities. In this work, we study the modularity from a combinatorial point of view. Our analysis (as the modularity definition) relies on the use of the configurational model, a technique that given a graph produces a series of randomized copies keeping the degree sequence invariant. We develop an approach that enumerates the null model partitions and can be used to calculate the probability distribution function of the modularity. Our theory allows for a deep inquiry of several interesting features characterizing modularity such as its resolution limit and the statistics of the partitions that maximize it. Additionally, the study of the probability of extremes of the modularity in the random graph partitions opens the way for a definition of the statistical significance of network partitions.

physics.soc-ph↗

arXiv2010

Statistical significance of communities in networks

Nodes in real-world networks are usually organized in local modules. These groups, called communities, are intuitively defined as sub-graphs with a larger density of internal connections than of external links. In this work, we introduce a new measure aimed at quantifying the statistical significance of single communities. Extreme and Order Statistics are used to predict the statistics associated with individual clusters in random graphs. These distributions allows us to define one community significance as the probability that a generic clustering algorithm finds such a group in a random graph. The method is successfully applied in the case of real-world networks for the evaluation of the significance of their communities.

physics.soc-ph↗

arXiv2010

Explosive percolation: a numerical analysis

Percolation is one of the most studied processes in statistical physics. A recent paper by Achlioptas et al. [Science 323, 1453 (2009)] has shown that the percolation transition, which is usually continuous, becomes discontinuous ("explosive") if links are added to the system according to special cooperative rules (Achlioptas processes). In this paper we present a detailed numerical analysis of Achlioptas processes with product rule on various systems, including lattices, random networks a' la Erdoes-Renyi and scale-free networks. In all cases we recover the explosive transition by Achlioptas et al.. However, the explosive percolation transition is kind of hybrid as, despite the discontinuity of the order parameter at the threshold, one observes traces of analytical behavior, like power law distributions of cluster sizes. In particular, for scale-free networks with degree exponent lambda<3, all relevant percolation variables display power law scaling, just as in continuous second-order phase transitions.

physics.soc-ph↗

arXiv2009

Explosive percolation in scale-free networks

We study scale-free networks constructed via a cooperative Achlioptas growth process. Links between nodes are introduced in the network in order to produce a scale-free graph with given exponent lambda for the degree distribution, but the choice of each new link depends on the mass of the clusters that this link will merge. Networks constructed via this biased procedure show a percolation transition which strongly differs from the one observed in standard percolation, where links are introduced just randomly. The different growth process leads to a phase transition with a non-vanishing percolation threshold already for lambda > lambda_c ~ 2.2. More interestingly, the transition is continuous when lambda <= 3 but becomes discontinuous when lambda > 3. This may have important consequences both for the structure of networks and for the dynamics of processes taking place on them.

physics.soc-ph↗

arXiv2009

Diffusion of scientific credits and the ranking of scientists

Recently, the abundance of digital data enabled the implementation of graph based ranking algorithms that provide system level analysis for ranking publications and authors. Here we take advantage of the entire Physical Review publication archive (1893-2006) to construct authors' networks where weighted edges, as measured from opportunely normalized citation counts, define a proxy for the mechanism of scientific credit transfer. On this network we define a ranking method based on a diffusion algorithm that mimics the spreading of scientific credits on the network. We compare the results obtained with our algorithm with those obtained by local measures such as the citation count and provide a statistical analysis of the assignment of major career awards in the area of Physics. A web site where the algorithm is made available to perform customized rank analysis can be found at the address http://www.physauthorsrank.org

physics.soc-ph↗

arXiv2009

Human Activity in the Web

The recent information technology revolution has enabled the analysis and processing of large-scale datasets describing human activities. The main source of data is represented by the Web, where humans generally use to spend a relevant part of their day. Here we study three large datasets containing the information about Web human activities in different contexts. We study in details inter-event and waiting time statistics. In both cases, the number of subsequent operations which differ by tau units of time decays power-like as tau increases. We use non-parametric statistical tests in order to estimate the significance level of reliability of global distributions to describe activity patterns of single users. Global inter-event time probability distributions are not representative for the behavior of single users: the shape of single users'inter-event distributions is strongly influenced by the total number of operations performed by the users and distributions of the total number of operations performed by users are heterogeneous. A universal behavior can be anyway found by suppressing the intrinsic dependence of the global probability distribution on the activity of the users. This suppression can be performed by simply dividing the inter-event times with their average values. Differently, waiting time probability distributions seem to be independent of the activity of users and global probability distributions are able to significantly represent the replying activity patterns of single users.

physics.soc-ph↗

arXiv2009

Renormalization flows in complex networks

Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the mathematical tools of statistical physics have proven to be particularly suitable for studying and understanding complex networks. Nevertheless, an important obstacle to this theoretical approach is still represented by the difficulties to draw parallelisms between network science and more traditional aspects of statistical physics. In this paper, we explore the relation between complex networks and a well known topic of statistical physics: renormalization. A general method to analyze renormalization flows of complex networks is introduced. The method can be applied to study any suitable renormalization transformation. Finite-size scaling can be performed on computer-generated networks in order to classify them in universality classes. We also present applications of the method on real networks.

physics.soc-ph↗

arXiv2008

Benchmark graphs for testing community detection algorithms

Community structure is one of the most important features of real networks and reveals the internal organization of the nodes. Many algorithms have been proposed but the crucial issue of testing, i.e. the question of how good an algorithm is, with respect to others, is still open. Standard tests include the analysis of simple artificial graphs with a built-in community structure, that the algorithm has to recover. However, the special graphs adopted in actual tests have a structure that does not reflect the real properties of nodes and communities found in real networks. Here we introduce a new class of benchmark graphs, that account for the heterogeneity in the distributions of node degrees and of community sizes. We use this new benchmark to test two popular methods of community detection, modularity optimization and Potts model clustering. The results show that the new benchmark poses a much more severe test to algorithms than standard benchmarks, revealing limits that may not be apparent at a first analysis.

physics.soc-ph↗

arXiv2008

Universality of citation distributions: towards an objective measure of scientific impact

We study the distributions of citations received by a single publication within several disciplines, spanning broad areas of science. We show that the probability that an article is cited $c$ times has large variations between different disciplines, but all distributions are rescaled on a universal curve when the relative indicator $c_f=c/c_0$ is considered, where $c_0$ is the average number of citations per article for the discipline. In addition we show that the same universal behavior occurs when citation distributions of articles published in the same field, but in different years, are compared. These findings provide a strong validation of $c_f$ as an unbiased indicator for citation performance across disciplines and years. Based on this indicator, we introduce a generalization of the h-index suitable for comparing scientists working in different fields.

physics.soc-ph↗

arXiv2008

Complex networks renormalization: flows and fixed points

Recently, it has been claimed that some complex networks are self-similar under a convenient renormalization procedure. We present a general method to study renormalization flows in graphs. We find that the behavior of some variables under renormalization, such as the maximum number of connections of a node, obeys simple scaling laws, characterized by critical exponents. This is true for any class of graphs, from random to scale-free networks, from lattices to hierarchical graphs. Therefore, renormalization flows for graphs are similar as in the renormalization of spin systems. An analysis of classic renormalization for percolation and the Ising model on the lattice confirms this analogy. Critical exponents and scaling functions can be used to classify graphs in universality classes, and to uncover similarities between graphs that are inaccessible to a standard analysis.

physics.soc-ph↗

arXiv2006

Phase transition between synchronous and asynchronous updating algorithms

We update a one-dimensional chain of Ising spins of length $L$ with algorithms which are parameterized by the probability $p$ for a certain site to get updated in one time step. The result of the update event itself is determined by the energy change due to the local change in the configuration. In this way we interpolate between the Metropolis algorithm at zero temperature for $p$ of the order of 1/L and for large $L$, and a synchronous deterministic updating procedure for $p=1$. As function of $p$ we observe a phase transition between the stationary states to which the algorithm drives the system. These are non-absorbing stationary states with antiferromagnetic domains for $p>p_c$, and absorbing states with ferromagnetic domains for $p\leq p_c$. This means that above this transition the stationary states have lost any remnants to the ferromagnetic Ising interaction. A measurement of the critical exponents shows that this transition belongs to the universality class of parity conservation.

cond-mat.other↗

arXiv2006

Universality class of triad dynamics on a triangular lattice

We consider triad dynamics as it was recently considered by Antal \emph{et al.} [T. Antal, P. L. Krapivsky, and S. Redner, Phys. Rev. E {\bf 72}, 036121 (2005)] as an approach to social balance. Here we generalize the topology from all-to-all to a regular one of a two-dimensional triangular lattice. The driving force in this dynamics is the reduction of frustrated triads in order to reach a balanced state. The dynamics is parameterized by a so-called propensity parameter $p$ that determines the tendency of negative links to become positive. As a function of $p$ we find a phase transition between different kind of absorbing states. The phases differ by the existence of an infinitely connected (percolated) cluster of negative links that forms whenever $p\leq p_c$. Moreover, for $p\leq p_c$, the time to reach the absorbing state grows powerlike with the system size $L$, while it increases logarithmically with $L$ for $p > p_c$. From a finite-size scaling analysis we numerically determine the critical exponents $β$ and $ν$ together with $γ$, $τ$, $σ$. The exponents satisfy the hyperscaling relations. We also determine the fractal dimension $d_f$ that fulfills a hyperscaling relation as well. The transition of triad dynamics between different absorbing states belongs to a universality class with new critical exponents. We generalize the triad dynamics to four-cycle dynamics on a square lattice. In this case, again there is a transition between different absorbing states, going along with the formation of an infinite cluster of negative links, but the usual scaling and hyperscaling relations are violated.

cond-mat.stat-mech↗

arXiv2006

Reducing Frustration in Spin Systems: Social Balance as an XOR-SAT problem

Reduction of frustration was the driving force in an approach to social balance as it was recently considered by Antal \emph{et al.} [ T. Antal, P. L. Krapivsky, and S. Redner, Phys. Rev. E {\bf 72}, 036121 (2005). ]. We generalize their triad dynamics to $k$-cycle dynamics for arbitrary integer $k$. We derive the phase structure, determine the stationary solutions and calculate the time it takes to reach a frozen state. The main difference in the phase structure as a function of $k$ is related to $k$ being even or odd. As a second generalization we dilute the all-to-all coupling as considered by Antal \emph{et al.} to a random network with connection probability $w<1$. ...

physics.soc-ph↗

arXiv2006

Reentrant Synchronization and Pattern Formation in Pacemaker-Entrained Kuramoto Oscillators

We study phase entrainment of Kuramoto oscillators under different conditions on the interaction range and the natural frequencies. In the first part the oscillators are entrained by a pacemaker acting like an impurity or a defect. We analytically derive the entrainment frequency for arbitrary interaction range and the entrainment threshold for all-to-all couplings. For intermediate couplings our numerical results show a reentrance of the synchronization transition as a function of the coupling range. The origin of this reentrance can be traced back to the normalization of the coupling strength. In the second part we consider a system of oscillators with an initial gradient in their natural frequencies, extended over a one-dimensional chain or a two-dimensional lattice. Here it is the oscillator with the highest natural frequency that becomes the pacemaker of the ensemble, sending out circular waves in oscillator-phase space. No asymmetric coupling between the oscillators is needed for this dynamical induction of the pacemaker property nor need it be distinguished by a gap in the natural frequency.

cond-mat.other↗

arXiv2006

Entrainment of Coupled Oscillators on Regular Networks by Pacemakers

We study Kuramoto oscillators, driven by one pacemaker, on $d$-dimensional regular topologies with nearest neighbor interactions. We derive the analytical expressions for the common frequency in the case of phase-locked motion and for the critical frequency of the pacemaker, placed at an arbitrary position in the lattice, so that above the critical frequency no phase-locked motion is possible. We show that the mere change in topology from an open chain to a ring induces synchronization for a certain range of pacemaker frequencies and couplings, while keeping the other parameters fixed. Moreover we demonstrate numerically that the critical frequency of the pacemaker decreases as a power of the linear size of the lattice with an exponent equal to the dimension of the system. This leads in particular to the conclusion that for infinite-dimensional topologies the critical frequency for having entrainment decreases exponentially with the size of the system, or, more generally, with the depth of the network, that is the average distance of the oscillators from the pacemaker.

cond-mat.other↗

arXiv2005

Kuramoto Oscillators on Chains, Rings and Cayley-trees

We study systems of Kuramoto oscillators, driven by one pacemaker, on $d$-dimensional regular topologies like linear chains, rings, hypercubic lattices and Cayley-trees. For the special cases of next-neighbor and infinite-range interactions, we derive the analytical expressions for the common frequency in the case of phase-locked motion and for the critical frequency of the pacemaker, placed at an arbitrary position on the lattice, so that above the critical frequency no phase-locked motion is possible. These expressions depend on the number of oscillators, the type of coupling, the coupling strength, and the range of interactions. In particular we show that the mere change in topology from an open chain with free boundary conditions to a ring induces synchronization for a certain range of pacemaker frequencies and couplings, keeping the other parameters fixed. We also study numerically the phase evolution above the critical eigenfrequency of the pacemaker for arbitrary interaction ranges and find some interesting remnants to phase-locked motion below the critical frequency.

cond-mat.stat-mech↗