gem-graph is for: GE-ometric directed M-ulti-GRAPH

(1) A geometric graph is a graph whose nodes have coordinates in a space

(2) It is directed if its bonds are arrows

(3) It is a multigraph if multiple arrows can be stacked from the same node to another

Note that 'directed' does not means 'oriented': a graph is oriented if one of its nodes is its root

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Geometric directed multigraphs have properties that make them suitable for the representation of complex phenomena.

gem-graph is a software that enables modelling with a geometric directed multigraph.

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Faced with the difficulty of calculating the evolution of complex systems defined by

• a great diversity of objects and
• a great diversity of interactions,

The gem-graph rationale is:

1. represent space

2. a discreet (non-continuous) space

3. a space whose all units are similar

4. links can be established between some of these units

• they allow drawing objects (isolated connex parts of the graph) and situations (relative positions of objects)
• for practical purposes, it is convenient to use arrows and to allow stacking many of them from the same node to another

5. an automaton, i.e. a set of states and transitions can rewrite this space

6. states can represent space

• here, space can be understand as a representation or approximation of a real space
• but a state can be a space as well as a text or any other set of symbols or writings (ex: tags) that can be drawn in the graph using the same encoding and a state can be an association of both.

7. transitions are all combinations of a single type of elementary transition

8. the coding of static information (states) and dynamic information (transitions) is distinct

• the purpose of this restriction is to maintain a strict homogeneity of the rules (cf. §7) which is the condition of their automatic management and edition.

9. no constraint on granularity: the scope of the arrows between space units is not limited

10. the computation is local, random, asynchronous

11. interfaces are possible with statistical and / or continuous fermion models:

• spaces are then superimposed and conditions on intensive local variables (concentrations, temperatures, flows, etc...) can be added to the specific conditions of the gem-graph.

12. interfaces are possible with representations of bosons:

• spaces are then superimposed and conditions on intensive local variables (flux, cross section, etc.) can be added to the specific conditions of the gem-graph.

13. the topology, the dimension and the magnitude of the space are not constrained

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Locos, formas modumque coherentiae omium rerum status depingit. Nihil aliud comprehendet. Eas res praecepta movet aut transformat. Nihil aliud facit. Quaedam tranformationes in sua potestate sunt. Aliae transformationes alii succedere debent. Interpositus status inter illas et istas jacet. Ab antecedente statu primarum ad sequentem statum secundarum iter nullius est nisi per suorum interpositum statum.

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Design: two converging, complementary and interdependent approaches:

• one goes from the available data structures and algorithms to the graph structure and the automaton it supports (synthetic or bottom-up approach)
• the other goes from the gem-graph automaton constraints to the available software tools (analytical or top-down approach)

today (28-03-2011) two texts are under development:

• questions about the architecture: identification and naming of the main parts of this program and data structures
• theoretical issues : Rewritten Geometric Directed Multigraphs Properties. (JS. dec 2017) This text could be a starting point for a publication

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