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The latter may occur even if the distance in the other direction between the same two vertices is defined. In the mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph geodesic) connecting them. This is also known as the geodesic distance or shortest-path ...
The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
[5] Oriented graphs are directed graphs having no opposite pairs of directed edges (i.e. at most one of (x, y) and (y, x) may be arrows of the graph). It follows that a directed graph is an oriented graph if and only if it has no 2-cycle. [6] Such a graph can be obtained by applying an orientation to an undirected graph.
A vertex in a directed graph whose second neighborhood is at least as large as its first neighborhood is called a Seymour vertex. [5]In the second neighborhood conjecture, the condition that the graph have no two-edge cycles is necessary, for in graphs that have such cycles (for instance the complete oriented graph) all second neighborhoods may be empty or small.
A directed graph with three vertices and four directed edges (the double arrow represents an edge in each direction). A directed graph or digraph is a graph in which edges have orientations. In one restricted but very common sense of the term, [5] a directed graph is an ordered pair = (,) comprising:
The nearest neighbor graph (NNG) is a directed graph defined for a set of points in a metric space, such as the Euclidean distance in the plane. The NNG has a vertex for each point, and a directed edge from p to q whenever q is a nearest neighbor of p, a point whose distance from p is minimum among all the given points other than p itself. [1]
In graph theory, reachability refers to the ability to get from one vertex to another within a graph. A vertex s {\displaystyle s} can reach a vertex t {\displaystyle t} (and t {\displaystyle t} is reachable from s {\displaystyle s} ) if there exists a sequence of adjacent vertices (i.e. a walk ) which starts with s {\displaystyle s} and ends ...
In general, a distance matrix is a weighted adjacency matrix of some graph. In a network, a directed graph with weights assigned to the arcs, the distance between two nodes of the network can be defined as the minimum of the sums of the weights on the shortest paths joining the two nodes (where the number of steps in the path is bounded). [2]
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