# Mediatic graphs

## TL;DR

The paper introduces mediatic graphs as a new axiomatic framework for representing media, establishing a bijection between media and mediatic graphs, thus revealing structural insights into media representations.

## Contribution

It defines mediatic graphs axiomatically and proves their equivalence to media, providing a new structural perspective on media representations.

## Key findings

- Any medium can be represented as a mediatic graph.
- A bijection exists between media and mediatic graphs on a given set.
- Mediatic graphs reveal structural properties of media.

## Abstract

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.