My research is focused on the area of complex systems.  A system is complex when its global properties cannot be simply inferred by extrapolation from the properties of its constituents. The interactions of the constituents are usually simple, but the heterogeneity of the interaction patterns, the presence of nonlinearity and feedback effects give rise to the emergence of global properties/phenomena, involving both the structure and the dynamics of the system. Such emergent properties were not originally designed or imposed to the system from outside, but are a genuine product of self-organization. Examples of complex systems are fractals (see figure), chaotic systems, animal and human societies, the World Wide Web, etc.

The famous Mandelbrot fractal, studied by Benoit Mandelbrot in 1979. Like all fractals, it is a self-similar geometric object, in which each part, however small, looks like the whole. 

The field of complex systems is, by its very nature, interdisciplinary. Complex system scientists include physicists, mathematicians, computer scientists, biologists and engineers, with frequent collaborations between scholars with different backgrounds. I am actively working on complex networks theory and applications, and on statistical physics modelling of social dynamics.


Complex networks


A complex network is a graph endowed with the following basic properties:

  • The distribution of the number of adjacent links to a node (degree) is broad, with a tail that often follows a power law
  • The diameter, i.e. the longest of the shortest paths between nodes, is fairly small, growing only logarithmically with the size of the network (small-world phenomenon)
  • The clustering coefficient, i.e. the fraction of closed triads centered at a node, is significantly higher than in a random network with the same number of nodes and links 

The field started in 1998 with the seminal paper of Duncan Watts and Steven Strogatz, in which they showed that several networks existing in nature, society and technology, have the small-world property. The interest in this research was boosted by the empirical discoveries of the group of Albert-László Barabási, revealing that most real networks have a degree distribution with a power law tail. In this way, there is no characteristic value for the degree of a node, that is why people call these graphs scale-free networks.  

In the last years, scholars have studied the properties of these networks, proposed models to explain their genesis and evolution, investigated how dynamical processes develop on these special graphs. For an account of the activity in this field we refer to the recent review by Boccaletti et al.  

I am especially interested in the problem of the identification of community structure in networks. Real networks display a structure characterized by groups of nodes, called communities or modules, such that nodes of each group share more connections with the other nodes of the group than with the rest of the network. Detecting communities can lead to the discovery of functional units of biological networks, like protein-protein interaction networks or metabolic networks,  and disclose unknown properties of nodes.  But the problem is hard and still open, in spite of the many approaches which have been suggested over the years. The main difficulty is that it is an ill-defined problem, where there is still confusion about the basic elements, from the definition of community to the evaluation of partitions. Further complications are represented by the fact that nodes can belong to different groups (overlapping communities) and that groups may in turn represent subunits of larger modules (hierarchical structure).  

I also study the structure and function of information networks, particularly of the web graph, i.e. the graph where the nodes represent documents of the World Wide Web and the links are the hyperlinks that allow to jump from one web page to another. In particular I investigate the interplay between the web graph structure, search engines and user behavior. 


Statistical physics of social dynamics 

Society is complex. Social interactions usually involve  few individuals, yet non-trivial  global phenomena can emerge. For instance, a consensus on some issue can be reached after many discussions between pairs of individuals or within small groups, even if the whole community is large. Similar dynamics can explain how people end up to share a common culture, or language. The global organization of the system can be achieved via simple local interactions between people, just like phase transitions are originated by elementary interactions between neighboring particles/spins. This parallelism is the motivation of the countless applications of statistical physics tools and models to describe large scale social phenomena, like opinion formation, cultural dissemination, language origin and evolution, emergence of hierarchies from initially egalitarian societies, etc.

My main goal is to lay solid foundations to the field, by characterizing large scale social phenomena by means of quantitative regularities. Only in this way it is possible to attempt a quantitative description of social phenomena, which is the best contribution that physicists could give. This can be accomplished by collecting and analyzing data referring to mass phenomena, like elections, marketing, etc. Some recent striking results on elections and voting behavior can be found here. Another possible avenue is to design controlled social experiments by means of the World Wide Web.