Directed graph

directed edgedirecteddigraphoutdegreeindegreearcin-degreedigraphsout-degreearcs
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 edges, where the edges have a direction associated with them.wikipedia
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Vertex (graph theory)

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 edges, where the edges have a direction associated with them.
In mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices).

Tournament (graph theory)

tournamentstournamenttransitive tournament
A tournament is a directed graph (digraph) obtained by assigning a direction for each edge in an undirected complete graph.

Complete graph

completecomplete connectivitycomplete digraph
A complete digraph is a directed graph in which every pair of distinct vertices is connected by a pair of unique edges (one in each direction).

Directed acyclic graph

acyclicDAGacyclic directed graph
In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG ) is a finite directed graph with no directed cycles.

Cycle (graph theory)

cyclecyclessimple cycle
A directed cycle in a directed graph is a non-empty directed trail in which the only repeated are the first and last vertices.

Flow network

network flownetworkaugmenting path
In graph theory, a flow network (also known as a transportation network) is a directed graph where each edge has a capacity and each edge receives a flow.


oriented tree
In other words, if we replace its directed edges with undirected edges, we obtain an undirected graph that is both connected and acyclic.

Signal-flow graph

signal flow graphsignal-flow analysisElements of signal flow graphs
A signal-flow graph or signal-flowgraph (SFG), invented by Claude Shannon, but often called a Mason graph after Samuel Jefferson Mason who coined the term, is a specialized flow graph, a directed graph in which nodes represent system variables, and branches (edges, arcs, or arrows) represent functional connections between pairs of nodes.

Rooted graph

Accessible pointed graphrootedaccessible pointed directed graph
Both directed and undirected versions of rooted graphs have been studied, and there are also variant definitions that allow multiple roots.

Category theory

Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).

Quiver (mathematics)

quiverPath algebraquivers
In mathematics, a quiver is a directed graph where loops and multiple arrows between two vertices are allowed, i.e. a multidigraph.


directed multigraphpseudographlabeled multigraph
More specifically, these entities are addressed as directed multigraphs (or multidigraphs).
In this case the multigraph would be a directed graph with pairs of directed parallel edges connecting cities to show that it is possible to fly both to and from these locations.

Flow graph (mathematics)

flow graphFlow graphs
A flow graph is a form of digraph associated with a set of linear algebraic or differential equations:

Control-flow graph

control flow graphcontrol flowCFG
: outdegree(A) > 1 or indegree(B) > 1 (or both).

Free category

freefree categoriesfreely
In mathematics, the free category or path category generated by a directed graph or quiver is the category that results from freely concatenating arrows together, whenever the target of one arrow is the source of the next.

State diagram

StatechartState machine diagramstate transition diagram
A classic form of state diagram for a finite state machine or finite automaton (FA) is a directed graph with the following elements (Q,Σ,Z,δ,q 0,F):

Path (graph theory)

pathpathsdirected path
If a path leads from x to y, then y is said to be a successor of x and reachable from x, and x is said to be a predecessor of y.
A directed path (sometimes called dipath ) in a directed graph is a finite or infinite sequence of edges which joins a sequence of distinct vertices, but with the added restriction that the edges be all directed in the same direction.

Incidence matrix

incidence relationincidence matricesincidence
Another matrix representation for a directed graph is its incidence matrix.
The incidence matrix of a directed graph is a n × m matrix B where n and m are the number of vertices and edges respectively, such that B i,j = −1 if the edge e j leaves vertex v i, 1 if it enters vertex v i and 0 otherwise (many authors use the opposite sign convention).

Digraph realization problem

directed graph realization problem
The directed graph realization problem is the problem of finding a directed graph with the degree sequence a given sequence of positive integer pairs.
Given pairs of nonnegative integers, the problem asks whether there is a labeled simple directed graph such that each vertex v_i has indegree a_i and outdegree b_i.

Network theory

network analysisnetworksnetwork
Network theory is the study of graphs as a representation of either symmetric relations or asymmetric relations between discrete objects.

Adjacency matrix

adjacency matricesbiadjacency matrixadjacency-matrix representation
The adjacency matrix of a multidigraph with loops is the integer-valued matrix with rows and columns corresponding to the vertices, where a nondiagonal entry a ij is the number of arrows from vertex i to vertex j, and the diagonal entry a ii is the number of loops at vertex i.
In directed graphs, the in-degree of a vertex can be computed by summing the entries of the corresponding column, and the out-degree can be computed by summing the entries of the corresponding row.

Connectivity (graph theory)

connectedconnected graphconnectivity
A directed graph is weakly connected (or just connected ) 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 called weakly connected if replacing all of its directed edges with undirected edges produces a connected (undirected) graph.

Orientation (graph theory)

orientationorientationsoriented graph
In graph theory, an orientation of an undirected graph is an assignment of a direction to each edge, turning the initial graph into a directed graph.

Branching factor

For a vertex, the number of head ends adjacent to a vertex is called the indegree of the vertex and the number of tail ends adjacent to a vertex is its outdegree (called "branching factor" in trees).
In computing, tree data structures, and game theory, the branching factor is the number of children at each node, the outdegree.