Random graphs
Random graphs are probability distributions over graphs. Equivalently, they are graphs built through a random process. They are used for different purposes, such as: proving existence of (deterministic) graphs with specific properties; modeling complex networks encountered in different areas, from biology to social sciences; characterizing the typical elements of graph ensambles. My research interest concerns inhomogeneous and geometric random graphs.

Geometric networks
Networks may often be embedded in metric spaces, where each vertex is assigned a position.  In real contexts, it is natural to expect that two nearby vertices connect more easily than two distant vertices. When this happens, we say that the network is geometric. I am interested in studying this kind of networks mathematically, analyzing the properties of geometric models and understanding what differs in presence or absence of geometry.

Network structure
Many real world networks have been found to be scale-free: they have a power-law degree distribution, meaning they are self-similar, with a global fractal structure. On the other hand, large network often possess non-trivial topological properties, which considerably complicate the local analysis of the system. Part of my work, is to reconstruct the local structure of different network models. Studying network motifs and clustering is one way to achieve such result.