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I've read many literature papers, but I still cannot understand their exact formalization definitions. Is their any difference among them or is there any relationship among them?

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  • $\begingroup$ Doesn't Wikipedia tell you all of this? $\endgroup$ Commented Dec 14, 2017 at 20:57
  • $\begingroup$ The paper you are reading will often give a definition for what a term precisely means in the context of that paper. $\endgroup$
    – Juho
    Commented Dec 17, 2017 at 11:29

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I've only ever heard of directed and undirected graphs, whose definitions can be found in Wikipedia. Rudimentary search reveals the following interpretations of unidirectional and bidirectional graphs; it is possible that these terms also have different interpretations:

  • A unidirectional graph is another name for an undirected graph.
  • A bidirectional graph is a directed graph obtained from an undirected graph by replacing each edge $\{x,y\}$ by a pair of edges $(x,y),(y,x)$.
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Well I'll try giving simple definitions, let's hope you get the idea with that:

Directed graphs: Are basically those graphs that have edges with directional arrows marked on them. They show which direction to move between the two vertices they connect.

Undirected graphs: Are just the opposite of directed graphs, as in the edges do not have any associated directional arrows with them.

Unidirectional Graph: Is a graph with edges which are directed only in one direction, like in the case of a directed graph.

Bidirectional Graph: Is a graph in which each edge is given an independent orientation (or direction, or arrow) at each end. Thus, there are three kinds of bidirected edges: those where the arrows point outward, towards the vertices, at both ends; those where both arrows point inward, away from the vertices; and those in which one arrow points away from its vertex and towards the opposite end, while the other arrow points in the same direction as the first, away from the opposite end and towards its own vertex.

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  • $\begingroup$ Wikipedia calls your bidirectional graphs bidirected. $\endgroup$ Commented Dec 13, 2017 at 23:31

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