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There is a lack of references for graph theory translation from French to English, yet if you have some, let me know, I would appreciate it.

I always have some difficulties to translate these technical terms, how do you translate in English:

dictionnaire des suivants et des précédents

which is an array telling for each vertex what is its following vertex or vertices.

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Well, first, dictionnaire could certainly be translated as array, but under some circumstances (principally computer programming) it might be better to translate as dictionary. In programming languages, a distinction is sometimes made between a dictionary, which is a list of key-value pairs, and an array, which is simply an ordered list.

Next, I think it is important to keep in mind that your graph is presumably directed. For an undirected graph, it would be meaningless to refer to the suivants vs the précédents. In this case, some sources refer to incoming neighbors vs. outgoing neighbors. However, predecessors and successors might be the best way of referring to this, as indicated in Wikipedia's glossary of graph theory.

So I would write array of predecessors and successors, or dictionary of predecessors and successors, depending on the context. If there is not potential for confusion, it might be acceptable to reference an array of neighbors.

It is worth noting that a mathematician would mostly likely speak instead of the adjacency matrix. Since you are asking a question about graph theory, you may already know what an adjacency matrix is, but if you don't, it is a matrix (essentially a two-layer-deep array) that represents the directed edges between two points. I am sure that for sparse graphs, this would be an inefficient representation for computing, but in any theoretical work, I would assume this would be the default.

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In computer science, that would probably be referred to as a "map" or "dictionary" between vertices. Alternatively, the structure as a whole sounds a lot like a "graph", either directed (that is, it matters whether it's A→B or B→A) or undirected (probably directed, since it sounds like it does matter), and either cyclic (A→B→A is permissible) or acyclic. Generally, computer science borrows a lot of terminology from math, especially graph theory, so that should be fine.

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