Complex Networks

The intense research activity conducted during the last ten years has shown that many real systems (biological, technological, social, etc.) can be usefully studied by modeling them as graphs or networks. A network is a general mathematical representation which consists in a set of nodes or vertices (i.e., the elements or units of the system) and a set of links or edges (i.e., pair interactions between the elements). Real networks generally show “complex” topological features: the distribution of the number of connections per node is broad (scale-free networks); the average distance between pairs of nodes grows logarithmically with the system size (small-word networks). Statistical physicists have been strongly involved in the research activity about complex networks and performed a lot of studies regarding both their topological and dynamical properties. A relevant part of my research activity is focusing on these subjects. I am particularly interested in the extensions of traditional models of statistical physics, generally defined on regular d-dimensional lattices, to networks. My recent works on real space renormalization in networks and explosive percolation in scale-free networks go in this direction. I have also performed analysis of dynamical systems defined on networks: (i) synchronization properties of weakly coupled oscillators in regular graphs; (ii) social balance in networks.

Community Structure of Complex Networks

Another important property shared by almost all real networks is the presence of an intrinsic modular structure. Connections among nodes are generally far from being randomly drawn and quite often real networks are locally organized in clusters or communities. A community is intuitively defined as a set of vertices with an internal density of connections higher than the density of links towards other nodes outside the community. During last years community detection has become a well defined topic of research involving many scientists (physicists, computer scientists, social scientists, etc.) and giving rise to the production of an high number of publications. The identification of communities in networks plays in fact a fundamental role for the deep understanding of their structural properties: depending on the nature of the system modeled as a network, communities may represent papers dealing with the same topic, as in the case of citation networks, sets of actors sharing common interests, as in the case of social networks, groups of proteins with similar functionalities, as in the case of protein interaction networks. I have performed several studies about the community structure of networks.

Citation Analysis

More recently, I have started to work on Bibliometrics. The possibility to define unbiased bibliometric indicators for the fair evaluation of the scientific performances of papers, scientists, institutions, etc. has attracted my attention for its practical relevance in modern science. Quantitative bibliometric indicators are in fact nowadays often used for the evaluation of candidates in scientific contests like those for the assignment of institutional positions, grants and awards. The recent availability of bibliographic data sets about scientific publications has stimulated the activity of scientists in the introduction of numerical indicators able to quantitatively assess the relevance of a paper, journal, scientist, etc. Examples of indices often used for these purposes are the Impact Factor, the h-index, etc. I have published several papers on this topic.