Bigraph
[1] They have applications in the modelling of distributed systems for ubiquitous computing and can be used to describe mobile interactions.
They have also been used by Robin Milner in an attempt to subsume Calculus of Communicating Systems (CCS) and π-calculus.
[3][4] Aside from nodes and (hyper-)edges, a bigraph may have associated with it one or more regions which are roots in the place forest, and zero or more holes in the place graph, into which other bigraph regions may be inserted.
Similarly, to nodes we may assign controls that define identities and an arity (the number of ports for a given node to which link-graph edges may connect).
In the link graph we define inner and outer names, which define the connection points at which coincident names may be fused to form a single link.
Formally speaking, each bigraph is an arrow in a symmetric partial monoidal category (usually abbreviated spm-category) in which the objects are these interfaces.
Ports and names of the interfaces are extended with a polarity (positive or negative) with the requirement that the direction of hyper-edges goes from negative to positive.
Directed bigraphs were introduced as a meta-model for describing computation paradigms dealing with locations and resource communication where a directed link-graph provides a natural description of resource dependencies or information flow.
Examples of areas of applications are security protocols,[8] resource access management,[9] and cloud computing.
[6] Bigraphs with sharing[10] are a generalisation of Milner's formalisation that allows for a straightforward representation of overlapping or intersecting spatial locations.
The definition of link graph is unaffected by the introduction of sharing.
Areas of application of bigraphs with sharing include wireless networking protocols,[11] real-time management of domestic wireless networks[12] and mixed reality systems.
