Mediatic graphs

Details Mediatic graphs Mediatic graphs

2007-04-07

arxiv.org/abs/0704.0994v3

Mathematics

Combinatorics

Four axioms replaced by two; two references added; Fig.6 corrected

Scientific paper

Any medium can be represented as an isometric subgraph of the hypercube, with each token of the medium represented by a particular equivalence class of arcs of the subgraph. Such a representation, although useful, is not especially revealing of the structure of a particular medium. We propose an axiomatic definition of the concept of a `mediatic graph'. We prove that the graph of any medium is a mediatic graph. We also show that, for any non-necessarily finite set S, there exists a bijection from the collection M of all the media on a given set S (of states) onto the collection G of all the mediatic graphs on S.

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