Examples of using Directed graph in English and their translations into Serbian
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Directed graph connectivity.
Relation to hypergraphs and directed graphs.
The tree is viewed as a directed graph that contains two directed edges for each edge in the tree.
In the asymmetric TSP, paths may not exist in both directions or the distances might be different,forming a directed graph.
Transitive closure of directed graphs(Warshall's algorithm).
For directed graphs,"path" has to be replaced with directed path and"cycle" with directed cycle.
In the context of graph theory,a weighted directed graph is often called a network.
A conventional directed graph can be thought of as a hypergraph with hyperedges each of which has two tentacles.
A directed acyclic graph is a directed graph with no directed cycles.
A directed graph is called a directed multigraph or multidigraph if it may have multiple arrows(and sometimes loops).
The strongly connected components of a directed graph G are its maximal strongly connected subgraphs.
Biadjacency matrices may be used to describe equivalences between bipartite graphs, hypergraphs, and directed graphs.
A symmetric digraph is a directed graph in which for every arrow that belongs to it, the corresponding inversed arrow also belongs to it.
The Floyd-Warshall algorithm can be used to solve the following problems, among others:Shortest paths in directed graphs(Floyd's algorithm).
The Schulze method constructs a complete directed graph in which the vertices represent the candidates and every two vertices are connected by an edge.
A directed graph is strongly connected or strong if it contains a directed path from x to y and a directed path from y to x for every pair of vertices}.
In general, signal-flow graphs, unlike the regular directed graphs described above, do not correspond to the topology of the physical arrangement of components.
A directed graph has an Eulerian cycle if and only if every vertex has equal in degree and out degree, and all of its vertices with nonzero degree belong to a single strongly connected component.
According to the solution of this problem(Trahtman 2009),a strongly connected directed graph in which all vertices have the same outdegree has a synchronizable edge coloring if and only if it is aperiodic.
An arbitrary directed graph may also be transformed into a DAG, called its condensation, by contracting each of its strongly connected components into a single supervertex.
A similar reinterpretation of adjacency matrices may be used to show a one-to-one correspondence between directed graphs(on a given number of labeled vertices, allowing self-loops) and balanced bipartite graphs, with the same number of vertices on both sides of the bipartition.
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).[2].
One can view the same problem graph-theoretically,by constructing a functional graph(that is, a directed graph in which each vertex has a single outgoing edge) the vertices of which are the elements of S and the edges of which map an element to the corresponding function value, as shown in the figure.
A directed graph is called a simple digraph if it has no multiple arrows(two or more edges that connect the same two vertices in the same direction) and no loops(edges that connect vertices to themselves).
Petri nets utilize the properties of bipartite directed graphs and other properties to allow mathematical proofs of the behavior of systems while also allowing easy implementation of simulations of the system.[39].
A directed graph is strongly connected or strong if it contains a directed path from x to y and a directed path from y to x for every pair of vertices{x, y}. The strong components are the maximal strongly connected subgraphs.
Definitions: G(V, E):weighted directed graph, with set of vertices V and set of directed edges E, w(u, v): cost of directed edge from node u to node v(costs are non-negative).
A directed graph is weakly connected(or just connected[4]) if the undirected underlying graph obtained by replacing all directed edges of the graph with undirected edges is a connected graph. .
It is also possible to check whether a given directed graph is a DAG in linear time, either by attempting to find a topological ordering and then testing for each edge whether the resulting ordering is valid or alternatively, for some topological sorting algorithms, by verifying that the algorithm successfully orders all the vertices without meeting an error condition.
A directed graph has an Eulerian trail if and only if at most one vertex has(out-degree)-(in-degree)= 1, at most one vertex has(in-degree)-(out-degree)= 1, every other vertex has equal in-degree and out-degree, and all of its vertices with nonzero degree belong to a single connected component of the underlying undirected graph. .