Network Science

The past two decades have witnessed the coming of age of network science as the central paradigm behind some of the most fascinating discoveries of the 21st century, from the mathematical formulation of small-world properties and their omnipresence in gene and transcriptional networks, protein networks, brain and social networks, food chains, and electric power grids, to the universal scaling properties due to growth and preferential attachment that likewise pervade biological, social, and technological networks. Network science has also provided models, methods, and algorithms that have revived not just mathematics and physics, but indeed many other fields of natural and social sciences.

In addition to the study of static networks that remain structurally unchanged, methods of network science allow us to study network evolution over time, for example due to changes in external factors, the onset of disease, targeted attack, or simply due to random failure. Such changes can be studied in the realm of temporal networks, where the theoretical framework accounts for the addition or removal of nodes, or similarly for changes in links between nodes, over time. It is also important that networks exist between different layers of each studied system, for example in biological systems, where networks of organelles form cells, which then again form networks to form organs, and so on. This can be accommodated in the theoretical framework of multilayer or interdependent networks, or more generally networks of networks, which acknowledge that not only are the interactions in complex systems limited and thus inadequately described by well-mixed models, but also that the networks that should be an integral part of such models are often interconnected, thus making the processes that are unfolding on them interdependent. From the world economy and transportation systems to social media, it is clear that processes taking place in one network can significantly affect what is happening in many other networks.

In addition to network science, technological breakthroughs in the acquisition and storage of vast amounts of digitized data have also aided the progress in all the above-mentioned disciplines. The so-called big data revolution has had a particularly deep impact on social sciences and economics, where social and behavioral experiments in the past typically involved one-shot self-reported data on relationships and their outcomes in a small sample of people, while today the approach is to mine massive amounts of digitized data for both the structure and content of relationships. Also in biological and chemical systems, advanced imaging techniques and increasingly sophisticated experimental equipment have led to a deluge of data, and thus to synergies of many other fields and network science.

Network Science is the Section of Mathematics devoted to publishing original research and reviews on everything networks, especially research at the interface of mathematics, physics, biology, sociology, data science, and network science, with a broad coverage as described by the keywords below.

We welcome submissions, and we will do our best for a fast and fair evaluation of all submitted research.

Prof. Dr. Matjaz Perc
Section Editor-in-Chief