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Shortest path (A, C, E, D, F) between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.
It should not be confused with the diameter of the network, which is defined as the longest geodesic, i.e., the longest shortest path between any two nodes in the network (see Distance (graph theory)). The average path length distinguishes an easily negotiable network from one, which is complicated and inefficient, with a shorter average path ...
A unit distance graph with 16 vertices and 40 edges. In mathematics, particularly geometric graph theory, a unit distance graph is a graph formed from a collection of points in the Euclidean plane by connecting two points whenever the distance between them is exactly one.
A metric space defined over a set of points in terms of distances in a graph defined over the set is called a graph metric. The vertex set (of an undirected graph) and the distance function form a metric space, if and only if the graph is connected. The eccentricity ϵ(v) of a vertex v is the greatest distance between v and any other vertex; in ...
In terms of a displacement-time (x vs. t) graph, the instantaneous velocity (or, simply, velocity) can be thought of as the slope of the tangent line to the curve at any point, and the average velocity as the slope of the secant line between two points with t coordinates equal to the boundaries of the time period for the average velocity.
A solution to the minimax path problem between the two opposite corners of a grid graph can be used to find the weak Fréchet distance between two polygonal chains. Here, each grid graph vertex represents a pair of line segments, one from each chain, and the weight of an edge represents the Fréchet distance needed to pass from one pair of ...
In graph theory, a geodetic graph is an undirected graph such that there exists a unique (unweighted) shortest path between each two vertices.. Geodetic graphs were introduced in 1962 by Øystein Ore, who observed that they generalize a property of trees (in which there exists a unique path between each two vertices regardless of distance), and asked for a characterization of them. [1]
The Fréchet distance between two concentric circles of radius and respectively is | |. The longest leash is required when the owner stands still and the dog travels to the opposite side of the circle ( r 1 + r 2 {\displaystyle r_{1}+r_{2}} ), and the shortest leash when both owner and dog walk at a constant angular velocity around the circle ...