## Scientific overview

In the last ten years, the study of complex networks has received an important boost with large interdisciplinary efforts aimed at their analysis and characterization. Two main points explain this large activity: on the one hand, many systems coming from very different disciplines (from biology to computer science) have a convenient representation in terms of graphs; on the other hand, the ever-increasing availability of large data sets and computer power have allowed their storage and manipulation. In particular, mapping projects of the World-Wide Web and the Internet have first given the opportunity to study the topology of large complex networks. Gradually, other maps have followed, describing many networks of practical interest in social science, critical infrastructures, and biology.

Graph theory has long been a branch of mathematics, and the paradigmatic Erdös-Renyi random graph thought to represent most networks. Through the systematic analysis and characterization of network representations of many different systems, researchers of several disciplines have however unveiled complex topologies and very heterogeneous structures, with connectivity patterns statistically characterized by heavy-tails and large fluctuations, scale-free properties, and non trivial correlations such as high clustering and hierarchical ordering. These properties make most real-world networks very different from the models used until then and well-known in graph theory, so that a large amount of work has been devoted to the development of new tools for network’s statistical characterization and modeling, in order to identify the most relevant properties of networks, and to understand which creation mechanisms could lead to these properties.

The research on the characterization, structure and modeling of complex networks has come from a largely interdisciplinary effort. First, as mentioned, many concepts come from graph theory. The large size and dynamic nature of complex networks has also attracted the attention of the statistical physics community. The statistical physics approach has been exploited as a very convenient strategy because of its deep connection with statistical graph theory and the possibility of characterizing emergent macroscopic phenomena in terms of the dynamical evolution of the basic elements of the system. Social sciences have moreover long been dealing with social networks[2], and widely used tools come directly from this literature. On another aspect, complex networks have also attracted researchers from the algorithmic point of view on the structural properties and on the complexity of methods suitable to handle very large complex networks. Finally, including a signal and image processing approach to study complex networks and data on networks is an emerging approach, that is particularly dynamic in Lyon.

Particularly important efforts are related to dynamical process occurring on top of social networks like the propagation of a disease, information, or the emergence of consensus e.g. in terms of opinion, or language usage. Epidemiologists, computer scientists, and social scientists share a common interest in studying spreading phenomena and rely on very similar models for the description of the diffusion of viruses, knowledge, and innovation. Strikingly, it turns out that the structure of complex networks has drastic consequences on the spreading process. In addition, many networks have a dynamical nature, with an evolution time scale that may be of the same order as the one of dynamical processes occurring between the nodes. For instance, people make new acquaintances, change their relations; the propagation of a virus or of information occurs on contact networks that are highly dynamical objects. In this spirit, a number of recent works have focused on the coevolution of networks: in these works, the dynamics of the network and on the network are entangled with feedback effects that can determine new interesting phenomenology. The recent availability of temporally resolved data has moreover allowed to uncover unexpected properties of evolving networks, opening the door to the new field of temporal networks.

These questions, which are in the focus of contemporary network science, set the scope of the actual proposal where we aim to bring together world-known experts from the fields of mathematics, physics, signal processing, computer science, social science, epidemiology and linguistic to discuss and enhance our understanding about the interaction between the structure, evolution, and coupled dynamical processes of complex networks.

## 2 Workshops & 1 Joint Conference

- Data Driven Approach to Networks and Linguistic, Lyon May 11-13 2016
- Processes On and Of Networks, Lyon June 20-22 2016
- Complex Networks: from theory to interdisciplinary applications, Marseille July 11-13 2016 as a satellite meeting to Statphys26

Note that at the end of the semester, the 26th IUPAP International conference on Statistical Physics, Statphys 26 will take place in Lyon from July, 18th to 22nd. The conference will cover a wide range of topics including traditional aspects of statistical mechanics, such as applications to hard and soft condensed matter, phase transitions, disordered systems and non-equilibrium physics, as well as emergent and modern applications such as turbulence, signal processing, complex systems and mathematics.