arXiv subjects

Santo Fortunato

Publications and source records attributed to Santo Fortunato.

At least 91 records · Page 5Linked to original sources

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

Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities

Many complex networks display a mesoscopic structure with groups of nodes sharing many links with the other nodes in their group and comparatively few with nodes of different groups. This feature is known as community structure and encodes precious information about the organization and the function of the nodes. Many algorithms have been proposed but it is not yet clear how they should be tested. Recently we have proposed a general class of undirected and unweighted benchmark graphs, with heterogenous distributions of node degree and community size. An increasing attention has been recently devoted to develop algorithms able to consider the direction and the weight of the links, which require suitable benchmark graphs for testing. In this paper we extend the basic ideas behind our previous benchmark to generate directed and weighted networks with built-in community structure. We also consider the possibility that nodes belong to more communities, a feature occurring in real systems, like, e. g., social networks. As a practical application, we show how modularity optimization performs on our new benchmark.

physics.soc-ph↗

arXiv2009

Statistical physics of social dynamics

Statistical physics has proven to be a very fruitful framework to describe phenomena outside the realm of traditional physics. The last years have witnessed the attempt by physicists to study collective phenomena emerging from the interactions of individuals as elementary units in social structures. Here we review the state of the art by focusing on a wide list of topics ranging from opinion, cultural and language dynamics to crowd behavior, hierarchy formation, human dynamics, social spreading. We highlight the connections between these problems and other, more traditional, topics of statistical physics. We also emphasize the comparison of model results with empirical data from social systems.

physics.soc-ph↗

arXiv2009

Detecting the overlapping and hierarchical community structure of complex networks

Many networks in nature, society and technology are characterized by a mesoscopic level of organization, with groups of nodes forming tightly connected units, called communities or modules, that are only weakly linked to each other. Uncovering this community structure is one of the most important problems in the field of complex networks. Networks often show a hierarchical organization, with communities embedded within other communities; moreover, nodes can be shared between different communities. Here we present the first algorithm that finds both overlapping communities and the hierarchical structure. The method is based on the local optimization of a fitness function. Community structure is revealed by peaks in the fitness histogram. The resolution can be tuned by a parameter enabling to investigate different hierarchical levels of organization. Tests on real and artificial networks give excellent results.

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↗

arXiv2008

Spectral centrality measures in complex networks

Complex networks are characterized by heterogeneous distributions of the degree of nodes, which produce a large diversification of the roles of the nodes within the network. Several centrality measures have been introduced to rank nodes based on their topological importance within a graph. Here we review and compare centrality measures based on spectral properties of graph matrices. We shall focus on PageRank, eigenvector centrality and the hub/authority scores of HITS. We derive simple relations between the measures and the (in)degree of the nodes, in some limits. We also compare the rankings obtained with different centrality measures.

physics.soc-ph↗

arXiv2007

Community Structure in Graphs

Graph vertices are often organized into groups that seem to live fairly independently of the rest of the graph, with which they share but a few edges, whereas the relationships between group members are stronger, as shown by the large number of mutual connections. Such groups of vertices, or communities, can be considered as independent compartments of a graph. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. The task is very hard, though, both conceptually, due to the ambiguity in the definition of community and in the discrimination of different partitions and practically, because algorithms must find ``good'' partitions among an exponentially large number of them. Other complications are represented by the possible occurrence of hierarchies, i.e. communities which are nested inside larger communities, and by the existence of overlaps between communities, due to the presence of nodes belonging to more groups. All these aspects are dealt with in some detail and many methods are described, from traditional approaches used in computer science and sociology to recent techniques developed mostly within statistical physics.

physics.soc-ph↗

arXiv2007

Motif-based communities in complex networks

Community definitions usually focus on edges, inside and between the communities. However, the high density of edges within a community determines correlations between nodes going beyond nearest-neighbours, and which are indicated by the presence of motifs. We show how motifs can be used to define general classes of nodes, including communities, by extending the mathematical expression of Newman-Girvan modularity. We construct then a general framework and apply it to some synthetic and real networks.

physics.comp-ph↗

arXiv2007

Scaling and universality in proportional elections

A most debated topic of the last years is whether simple statistical physics models can explain collective features of social dynamics. A necessary step in this line of endeavour is to find regularities in data referring to large scale social phenomena, such as scaling and universality. We show that, in proportional elections, the distribution of the number of votes received by candidates is a universal scaling function, identical in different countries and years. This finding reveals the existence in the voting process of a general microscopic dynamics that does not depend on the historical, political and/or economical context where voters operate. A simple dynamical model for the behaviour of voters, similar to a branching process, reproduces the universal distribution.

physics.soc-ph↗

arXiv2007

Quality functions in community detection

Community structure represents the local organization of complex networks and the single most important feature to extract functional relationships between nodes. In the last years, the problem of community detection has been reformulated in terms of the optimization of a function, the Newman-Girvan modularity, that is supposed to express the quality of the partitions of a network into communities. Starting from a recent critical survey on modularity optimization, pointing out the existence of a resolution limit that poses severe limits to its applicability, we discuss the general issue of the use of quality functions in community detection. Our main conclusion is that quality functions are useful to compare partitions with the same number of modules, whereas the comparison of partitions with different numbers of modules is not straightforward and may lead to ambiguities.

physics.soc-ph↗

arXiv2006

Random Walks on Directed Networks: the Case of PageRank

PageRank, the prestige measure for Web pages used by Google, is the stationary probability of a peculiar random walk on directed graphs, which interpolates between a pure random walk and a process where all nodes have the same probability of being visited. We give some exact results on the distribution of PageRank in the cases in which the damping factor q approaches the two limit values 0 and 1. When q -> 0 and for several classes of graphs the distribution is a power law with exponent 2, regardless of the in-degree distribution. When q -> 1 it can always be derived from the in-degree distribution of the underlying graph, if the out-degree is the same for all nodes.

physics.soc-ph↗

arXiv2006

The egalitarian effect of search engines

Search engines have become key media for our scientific, economic, and social activities by enabling people to access information on the Web in spite of its size and complexity. On the down side, search engines bias the traffic of users according to their page-ranking strategies, and some have argued that they create a vicious cycle that amplifies the dominance of established and already popular sites. We show that, contrary to these prior claims and our own intuition, the use of search engines actually has an egalitarian effect. We reconcile theoretical arguments with empirical evidence showing that the combination of retrieval by search engines and search behavior by users mitigates the attraction of popular pages, directing more traffic toward less popular sites, even in comparison to what would be expected from users randomly surfing the Web.

cs.CY↗

arXiv2006

Resolution limit in community detection

Detecting community structure is fundamental to clarify the link between structure and function in complex networks and is used for practical applications in many disciplines. A successful method relies on the optimization of a quantity called modularity [Newman and Girvan, Phys. Rev. E 69, 026113 (2004)], which is a quality index of a partition of a network into communities. We find that modularity optimization may fail to identify modules smaller than a scale which depends on the total number L of links of the network and on the degree of interconnectedness of the modules, even in cases where modules are unambiguously defined. The probability that a module conceals well-defined substructures is the highest if the number of links internal to the module is of the order of \sqrt{2L} or smaller. We discuss the practical consequences of this result by analyzing partitions obtained through modularity optimization in artificial and real networks.

physics.soc-ph↗

arXiv2006

Is the intrinsic disorder of proteins the cause of the scale-free architecture of protein-protein interaction networks?

In protein-protein interaction networks certain topological properties appear to be recurrent: networks maps are considered scale-free. It is possible that this topology is reflected in the protein structure. In this paper we investigate the role of protein disorder in the network topology. We find that the disorder of a protein (or of its neighbors) is independent of its number of protein-protein interactions. This result suggests that protein disorder does not play a role in the scale-free architecture of protein networks.

q-bio.GN↗

arXiv2006

Scale-free network growth by ranking

Network growth is currently explained through mechanisms that rely on node prestige measures, such as degree or fitness. In many real networks those who create and connect nodes do not know the prestige values of existing nodes, but only their ranking by prestige. We propose a criterion of network growth that explicitly relies on the ranking of the nodes according to any prestige measure, be it topological or not. The resulting network has a scale-free degree distribution when the probability to link a target node is any power law function of its rank, even when one has only partial information of node ranks. Our criterion may explain the frequency and robustness of scale-free degree distributions in real networks, as illustrated by the special case of the Web graph.

cond-mat.dis-nn↗