My research mainly concerns the analysis and the modeling of large-scale networks encountered in practice. My work aims at proposing new tools stemming from graph theory in order to identify non-trivial properties of these networks and to define new models able to capture them. In this context, I recently proposed and studied models for the topology of the Internet, the routing at the IP level, mobile networks, legal networks and diffusion phenomena. I also work on metrology and analysis issues related to these networks.
Bipartite graphs
One of the motivation for properly identifying the properties of a network lies in our ability to use models for graphs generation that can produce similar structures. This is crucial not only to provide effective support for simulations but also to improve the understanding of the observed properties. The difficulty lies especially in the fact that the properties studied must emerge from the model and not just be the result of properly tuned parameters. As such, my work based on bipartite graphs showed the relevance of this approach both to propose models for the generation of random structures in which a wide range of properties emerge naturally but also to enable the analysis of new network properties. In particular, I was able to highlight the impact of the redundancy existing at the bipartite level on the observed properties of simple graph. The perspectives open by this work led me to propose recently a tripartite model able to generate bipartite structures closer to those observed in real networks.
Dynamics of networks
The problem described above deals with the structure of a network at a given time. But of course networks are constantly evolving. The nodes and the links of the networks are constantly changing. A second area of my research has focused on issues related to network dynamics and more particularly to the routing in the at the IP level in the Internet. Data collected by the team with the Radar tool make it possible to capture the dynamics of the routing as seen from a monitor connected to the Internet towards a set of destinations. These datasets are presented as routing trees measured with a high frequency and on a long period of time. They enabled to propose a first model of IP-level routing dynamics. This model attempts to account for both phenomena related to the load-balancing on the network and changes that occur in the underlying topology. In addition, it allowed to characterize the impact of the topology on the dynamics observed and specify the one of the frequency of measurements.
Diffusion phenomena
Understanding the spread of information on communication networks has now become a key issue, both from a theoretical and applied perspective. Despite the efforts of the scientific community to propose models that can account for this phenomenon, gauging them with large-scale real-world data remains an important challenge due to the scarcity of open, extensive and detailed data. Recently, I have developed a line of research that exploits traces of exchanges in peer-to-peer file systems to conduct simulations assessing the relevance of the classical SIR model. The results show that it is unable to account for most of the related diffusion properties, even when considering natural extensions such as the heterogeneity due to the activity of peers or the popularity of the file. These findings raise an alert against the careless, widespread use of this model but a recent work led me show that using the available temporal data in the traces and integrating it into an heterogeneous version of the diffusion model enables to improve its relevance in this context.
