High-dimensional inference is a rich field of modern statistics. One particularly important high-dimensional object is a network. It has become a pervasive model for many complex systems. There are various network models, that each have their special uses within their respective fields. Social scientists use ERGMs, probabilists like stochastic-block models and Erdos-Renyi graphs, systems’ people consider networks of differential equations, biologists use graphical models. For each of these models, it is often highly non-trivial to infer the parameters for the systems, based on (typically) limited available data. 

We strongly argue that high-dimensional inference of large graphs is a fruitful field of mathematics with an abundance of potential applications, stretching from epidemiology (infectious diseases), social sciences (social networks), neuroscience (brain networks), engineering (power networks), biology (genetic networks) to finance (financial networks). Advances are to be made in:

• asymptotic inference theory (what type of networks remain estimable with limited amounts of data)
• penalized inference theory (sparse inference of features of networks)
• computational considerations and distributed computing of inference procedures
• sampling theory on/in network populations
• visualisation, visual analysis and exploration of large networks