In the

mathematical Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

domain of

graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conn ...

, a bidirected graph (introduced by ). Reprinted in ''Combinatorial Optimization — Eureka, You Shrink!'', Springer-Verlag, Lecture Notes in Computer Science 2570, 2003, pp. 27–30, . is a

graph Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discre ...

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. Edges of these three types may be called, respectively, extraverted, introverted, and directed. The "directed" edges are the same as ordinary directed edges in a

directed graph In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed edges, often called arcs. Definition In formal terms, a directed graph is an ordered pa ...

; thus, a directed graph is a special kind of bidirected graph. It is sometimes desirable to have also edges with only one end (half-edges); these get only one arrow. An edge with no ends (a loose edge) has no arrows. The edges that are neither half nor loose edges may be called ordinary edges. A

skew-symmetric graph 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 p ...

is the double covering graph of a bidirected graph. A bidirected graph may be regarded as an orientation of a

signed graph In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. A signed graph is balanced if the product of edge signs around every cycle is positive. The name "signed graph" and the no ...

, similarly to how a directed graph may be viewed as an orientation of an ordinary

undirected graph In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called '' ve ...

Other meanings

A symmetric

(that is, a directed graph in which the reverse of every edge is also an edge) is sometimes also called a "bidirected graph".

References

Extensions and generalizations of graphs {{combin-stub

Other meanings

See also

References