Dynamics and Structure of Networks

Networks permeate virtually all areas of science and technology, from the internet to social networks and the genetic networks that determine our existence. The aim of the EU-funded DYNASNET project is to engage leading experts in network science and graph theory to build a mathematically sound theory of dynamic networks. The aim is to better analyse, predict and control the behaviour of real networks. Both network science and graph theory have achieved notable progress over the past decade: network science has offered a data-based topological approach for modelling complex networks. The project's work could rewrite our understanding of complex systems, with applications in a wide array of fields.

Objective

Networks define our life, being essential to cell biology, communications, social and economic systems, and impacting virtually all areas of science and technology. The aim of this proposal is to engage leading experts in network science and graph theory to build a mathematically sound theory of dynamical networks, which will be transformative to our understanding of complex systems, with applications in multiple disciplines.
Both fields have made major conceptual advances in the past decade: network science has offered a data-based basic topological description of complex networks, and has started to address the inherently dynamical nature of real networks, their reconstruction and control; in mathematics we have seen major advances in graph limit theory, the local-global dichotomy in observation, and promising steps in the theory of graphs with intermediate degrees, that capture real networks. While these concepts offer different formalisms to capture the same underlying reality, there has been no conversation between the two communities, limiting our understanding of real networks.
The proposed research aims to build on these advances to construct a coherent theory of dynamical networks, and to exploit its applications and predictive power to various real systems. We plan to offer a sound mathematical foundation of network science, helping us better analyze, predict and control the behavior of real networks. It will benefit mathematics in leading to an enriched, robust graph limit theory, with exciting applications in multiple areas of mathematics. To enhance the wider impact of the proposed mathematical advances, we plan to conduct a permanent conversation with experts from different domains that encounter and explore real networks, from cell biology to brain science and transportation and communication networks, inspiring with novel questions and helping the application of our advances in these domains.