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.

In recent years the research community has accumulated overwhelming evidence for the emergence of complex and heterogeneous connectivity patterns in a wide range of biological and socio-technical systems. The complex properties of real-world networks have a profound impact on the behavior of equilibrium and non-equilibrium phenomena occurring in various systems, and the study of epidemic spreading is central to our understanding of the unfolding of dynamical processes in complex networks. The theoretical analysis of epidemic spreading in heterogeneous networks requires the development of novel analytical frameworks, and it has produced results of conceptual and practical relevance. Here, we present a coherent and comprehensive review of the vast research activity concerning epidemic processes, detailing the successful theoretical approaches as well as making their limits and assumptions clear. Physicists, mathematicians, epidemiologists, computer and social scientists share a common interest in studying epidemic spreading and rely on very similar models for the description of the diffusion of pathogens, knowledge and innovation. For this reason, while we focus on the main results and the paradigmatic models in infectious disease modeling, we also present the major results concerning generalized social contagion processes. Finally, we outline the research activity at the forefront in the study of epidemic spreading in co-evolving, coupled and time-varying networks.

The investigation of community structures in networks is an important issue in many domains and disciplines. This problem is relevant for social tasks (objective analysis of relationships on the web), biological inquiries (functional studies in metabolic and protein networks), or technological problems (optimization of large infrastructures). Several types of algorithms exist for revealing the community structure in networks, but a general and quantitative definition of community is not implemented in the algorithms, leading to an intrinsic difficulty in the interpretation of the results without any additional nontopological information. In this article we deal with this problem by showing how quantitative definitions of community are implemented in practice in the existing algorithms. In this way the algorithms for the identification of the community structure become fully self-contained. Furthermore, we propose a local algorithm to detect communities which outperforms the existing algorithms with respect to computational cost, keeping the same level of reliability. The algorithm is tested on artificial and real-world graphs. In particular, we show how the algorithm applies to a network of scientific collaborations, which, for its size, cannot be attacked with the usual methods. This type of local algorithm could open the way to applications to large-scale technological and biological systems.

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 c0 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.bibliometrics ͉ analysis ͉ h index