Search results
Results from the WOW.Com Content Network
The weighted shortest-path distance generalises the geodesic distance to weighted graphs. In this case it is assumed that the weight of an edge represents its length or, for complex networks the cost of the interaction, and the weighted shortest-path distance d W ( u , v ) is the minimum sum of weights across all the paths connecting u and v .
The numbers beside the vertices indicate the distance from the root vertex. In mathematics and computer science, a shortest-path tree rooted at a vertex v of a connected, undirected graph G is a spanning tree T of G, such that the path distance from root v to any other vertex u in T is the shortest path distance from v to u in G.
The shortest-path graph with t = 2. In mathematics and geographic information science, a shortest-path graph is an undirected graph defined from a set of points in the Euclidean plane. The shortest-path graph is proposed with the idea of inferring edges between a point set such that the shortest path taken over the inferred edges will roughly ...
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.
Dijkstra's algorithm (/ ˈ d aɪ k s t r ə z / DYKE-strəz) is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, a road network.
For any undirected connected graph G, the set V of vertices of G can be turned into a metric space by defining the distance between vertices x and y to be the length of the shortest edge path connecting them. This is also called shortest-path distance or geodesic distance.
In the symmetric TSP, the distance between two cities is the same in each opposite direction, forming an undirected graph. This symmetry halves the number of possible solutions. In the asymmetric TSP, paths may not exist in both directions or the distances might be different, forming a directed graph. Traffic congestion, one-way streets, and ...
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]