  In modern cloud-based architectures, containers play a central role: they
provide powerful isolation mechanisms such that developers can focus on the
logic and dependencies of applications while system administrators can focus on
deployment and management issue. In this work, we propose a formal model for
container-based systems, using the framework of Bigraphical Reactive Systems
(BRSs). We first introduce local directed bigraphs, a graph-based formalism
which allows us to deal with localized resources. Then, we define a signature
for modelling containers and provide some examples of bigraphs modelling
containers. These graphs can be analysed and manipulated using techniques from
graph theory: properties about containers can be formalized as properties of
the corresponding bigraphic representations. Moreover, it turns out that the
composition of containers as performed by e.g. docker-compose, corresponds
precisely to the composition of the corresponding bigraphs inside an
``environment bigraph'' which in turn is obtained directly from the YAML file
used to define the composition of containers.
