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A directed graph is weakly connected (or just connected [9]) if the undirected underlying graph obtained by replacing all directed edges of the graph with undirected edges is a connected graph. A directed graph is strongly connected or strong if it contains a directed path from x to y (and from y to x) for every pair of vertices (x, y).
The different types of edge in a bidirected graph. In the mathematical domain of graph theory, a bidirected graph (introduced by Edmonds & Johnson 1970) [1] 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 ...
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).
An undirected hypergraph (,) is an undirected graph whose edges connect not just two vertices, but an arbitrary number. [2] An undirected hypergraph is also called a set system or a family of sets drawn from the universal set. Hypergraphs can be viewed as incidence structures.
It is a directed or undirected graph consisting of vertices, which represent concepts, and edges, which represent semantic relations between concepts, [1] mapping or connecting semantic fields. A semantic network may be instantiated as, for example, a graph database or a concept map .
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.
In an undirected graph, reachability between all pairs of vertices can be determined by identifying the connected components of the graph. Any pair of vertices in such a graph can reach each other if and only if they belong to the same connected component; therefore, in such a graph, reachability is symmetric ( s {\displaystyle s} reaches t ...
A totally cyclic orientation of a graph G is an orientation in which each edge belongs to a directed cycle. For connected graphs, this is the same thing as a strong orientation, but totally cyclic orientations may also be defined for disconnected graphs, and are the orientations in which each connected component of G becomes strongly connected ...