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A simple directed acyclic graph A tournament on 4 vertices. Symmetric directed graphs are directed graphs where all edges appear twice, one in each direction (that is, for every arrow that belongs to the digraph, the corresponding inverse arrow also belongs to it).
Additional families of symmetric graphs with an even number of vertices 2n, are the evenly split complete bipartite graphs K n,n and the crown graphs on 2n vertices. Many other symmetric graphs can be classified as circulant graphs (but not all). The Rado graph forms an example of a symmetric graph with infinitely many vertices and infinite degree.
In graph theory, a branch of mathematics, a skew-symmetric graph is a directed graph that is isomorphic to its own transpose graph, the graph formed by reversing all of its edges, under an isomorphism that is an involution without any fixed points. Skew-symmetric graphs are identical to the double covering graphs of bidirected graphs.
A directed graph is called an oriented graph if none of its pairs of vertices is linked by two mutually symmetric edges. Among directed graphs, the oriented graphs are the ones that have no 2-cycles (that is at most one of (x, y) and (y, x) may be arrows of the graph). [1] A tournament is an orientation of a complete graph.
Pages in category "Directed graphs" ... Table of vertex-symmetric digraphs; Tournament (graph theory) Transpose graph; Trophic coherence; W. Wait-for graph; Why ...
The Laplacian matrix of a directed graph is by definition generally non-symmetric, while, e.g., traditional spectral clustering is primarily developed for undirected graphs with symmetric adjacency and Laplacian matrices. A trivial approach to apply techniques requiring the symmetry is to turn the original directed graph into an undirected ...
A directed graph with three vertices and four directed edges (the double arrow represents an edge in each direction). A directed graph or digraph is a graph in which edges have orientations. In one restricted but very common sense of the term, [5] a directed graph is an ordered pair = (,) comprising:
The adjacency matrix can be used to determine whether or not the graph is connected. If a directed graph has a nilpotent adjacency matrix (i.e., if there exists n such that A n is the zero matrix), then it is a directed acyclic graph. [10]