Networks are often used as representations of complex data sets. In order to understand such representations, random network models are a useful tool. Randomness in networks is typically included by fixing a vertex set and modelling the collection of edge indicator variables via a random model. Interesting probabilistic questions arise from such models; even the typical behaviour of the number of subgraphs of certain types can be challenging.
Another problem area is that of comparing networks in a meaningful way; answers to this question could be used to try to tease out evolutionary information from protein interaction networks. A third area of research is synthetic data generation: given a network, how can we generate synthetic networks which capture essentials of the given network without being identical to it, and can we give theoretical guarantees for such network generators?
Limiting behaviours under different regimes are also a very active area of research.
Much of Gesine Reinert's work is focussed on network analysis.