Statistica Neerlandica special issue on Statistical Network Science

We are pleased to present you here with a special issue of Statistica Neerlandica on Statistical Network Science. Ironically, while we are writing this editorial at home, a contagion process is spreading across people's contact networks with a speed that has surprised many. Governments are trying desperately to contain the most devastating effects of the COVID-19 epidemic by limiting contacts between people. At the same time, epidemiologists are trying to learn from imperfect screening data about the infection fatality rates in various parts of the population, about whether the disease can be asymptomatic and how quickly the virus spreads. Although many things are not yet clear, the coronavirus pandemic has shown that there is much more to learn about these types of processes. For the past 4 years, the EU COST Action COSTNET (CA15109) has brought together European statisticians and other quantitative scientists to study all kinds of processes in and on networks. From infectious disease networks, social networks, graphical models, phylogenetic trees, financial networks, and brain networks, the COST Action has been studying communalities and possible synergies between various approaches and, in the process, it has established a healthy community of over 500 network data scientists. This is a truly open effort to advance an important field of science through the grassroots EU COST funding scheme, allowing scientists to join also after the funding had been granted. In this special issue, people from within and outside the COST Action have created a beautiful mosaic of many of the issues that have been studied in the past 4 years. We begin, appropriately, with two papers on infectious disease modeling. Britton provides an overview of epidemic models on social networks, discussing common transmission mechanisms, introducing the now well-known basic reproduction number R0 and providing ways to perform inference in these models. Hansson and Strömdahl consider the special case of sexually transmitted diseases and how to infer transmission properties when we observe only the immediate neighborhood of the sampled individuals, the so-called ego-centric networks. Still a biological network but with a focus on evolutionary processes, Richter and coauthors focus on modeling the spreading process of evolution by means of speciations and extinctions. The challenge in such networks is the almost complete absence of information about extinct species, which severely biases naïve estimates of the dynamics in such processes. Many processes on networks, such as those described above, are inherently dynamic and specific methodologies have been developed to capture this. Fritz and coauthors provide a comprehensive overview of both discrete and continuous time network models. They contrast temporal exponential random graph models (s-TERGMs) in discrete time with relational event models (REMs) in continuous time and show how existing software implementations can be used to analyze dynamic network evolutions. Snijders and coauthors also explore dynamic network