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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).
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).
Let G = (V, E, Φ) be a directed graph. A directed circuit is a non-empty directed trail (e 1, e 2, ..., e n) with a vertex sequence (v 1, v 2, ..., v n, v 1). A directed cycle or simple directed circuit is a directed circuit in which only the first and last vertices are equal. [1] n is called the length of the directed circuit resp. length of ...
Directed graphs as defined in the two definitions above cannot have loops, because a loop joining a vertex to itself is the edge (for a directed simple graph) or is incident on (for a directed multigraph) (,) which is not in {(,) (,)}. So to allow loops the definitions must be expanded.
(However, as directed graphs, tournaments are not complete: complete directed graphs have two edges, in both directions, between each two vertices. [1]) The name tournament comes from interpreting the graph as the outcome of a round-robin tournament, a game where each player is paired against every other exactly once. In a tournament, the ...
A "simple directed path" is a path where all vertices are distinct. A weighted directed graph associates a value (weight) with every edge in the directed graph. The weight of a directed walk (or trail or path) in a weighted directed graph is the sum of the
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Finally, it is clearly NP-hard on all graph classes on which the Hamiltonian path problem is NP-hard, such as on split graphs, circle graphs, and planar graphs. A simple model of a directed acyclic graph is the Price model, developed by Derek J. de Solla Price to represent citation networks. This is simple enough to allow for analytic results ...