  Networks serve as a tool used to examine the large-scale connectivity
patterns in complex systems. Modelling their generative mechanism
nonparametrically is often based on step-functions, such as the stochastic
block models. These models are capable of addressing two prominent topics in
network science: link prediction and community detection. However, such methods
often have a resolution limit, making it difficult to separate small-scale
structures from noise. To arrive at a smoother representation of the network's
generative mechanism, we explicitly trade variance for bias by smoothing blocks
of edges based on stochastic equivalence. As such, we propose a different
estimation method using a new model, which we call the stochastic shape model.
Typically, analysis methods are based on modelling node or link communities. In
contrast, we take a hybrid approach, bridging the two notions of community.
Consequently, we obtain a more parsimonious representation, enabling a more
interpretable and multiscale summary of the network structure. By considering
multiple resolutions, we trade bias and variance to ensure that our estimator
is rate-optimal. We also examine the performance of our model through
simulations and applications to real network data.
