  The aim of this paper is to derive macroscopic equations for processes on
large co-evolving networks, examples being opinion polarization with the
emergence of filter bubbles or other social processes such as norm development.
This leads to processes on graphs (or networks), where both the states of
particles in nodes as well as the weights between them are updated in time. In
our derivation we follow the basic paradigm of statistical mechanics: We start
from paradigmatic microscopic models and derive a Liouville-type equation in a
high-dimensional space including not only the node states in the network
(corresponding to positions in mechanics), but also the edge weights between
them. We then derive a natural (finite) marginal hierarchy and pass to an
infinite limit.
  We will discuss the closure problem for this hierarchy and see that a simple
mean-field solution can only arise if the weight distributions between nodes of
equal states are concentrated. In a more interesting general case we propose a
suitable closure at the level of a two-particle distribution (including the
weight between them) and discuss some properties of the arising kinetic
equations. Moreover, we highlight some structure-preserving properties of this
closure and discuss its analysis in a minimal model. We discuss the application
of our theory to some agent-based models in literature and discuss some open
mathematical issues.
