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A semicomplete digraph is a quasi-transitive digraph. There are extensions of quasi-transitive digraphs called k-quasi-transitive digraphs. [5] Oriented graphs are directed graphs having no opposite pairs of directed edges (i.e. at most one of (x, y) and (y, x) may be arrows of the graph).
The directed graph (or digraph) on the right is an orientation of the undirected graph on the left. In graph theory, an orientation of an undirected graph is an assignment of a direction to each edge, turning the initial graph into a directed graph.
The best known vertex transitive digraphs (as of October 2008) in the directed Degree diameter problem are tabulated below. Table of the orders of the largest known vertex-symmetric graphs for the directed degree diameter problem
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
A flow graph is more general than a directed network, in that the edges may be associated with gains, branch gains or transmittances, or even functions of the Laplace operator s, in which case they are called transfer functions. [2] There is a close relationship between graphs and matrices and between digraphs and matrices. [9] "The algebraic ...
The Art of Computer Programming defines rooted digraphs slightly more broadly, namely, a directed graph is called rooted if it has at least one node that can reach all the other nodes. Knuth notes that the notion thus defined is a sort of intermediate between the notions of strongly connected and connected digraph .
A signed digraph is a directed graph with signed arcs. Signed digraphs are far more complicated than signed graphs, because only the signs of directed cycles are significant. For instance, there are several definitions of balance, each of which is hard to characterize, in strong contrast with the situation for signed undirected graphs.
In mathematics, the free category or path category generated by a directed graph or quiver is the category that results from freely concatenating arrows together, whenever the target of one arrow is the source of the next. More precisely, the objects of the category are the vertices of the quiver, and the morphisms are paths between objects.