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During execution, the distance of a node N is the length of the shortest path discovered so far between the starting node and N. [ 18 ] From the unvisited set, select the current node to be the one with the smallest (finite) distance; initially, this is the starting node (distance zero).
Shortest path (A, C, E, D, F), blue, 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. [1]
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 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 ...
Specifically, a small-world network is defined to be a network where the typical distance L between two randomly chosen nodes (the number of steps required) grows proportionally to the logarithm of the number of nodes N in the network, that is: [2] while the global clustering coefficient is not small.
Two primary problems of pathfinding are (1) to find a path between two nodes in a graph; and (2) the shortest path problem—to find the optimal shortest path. Basic algorithms such as breadth-first and depth-first search address the first problem by exhausting all possibilities; starting from the given node, they iterate over all potential ...
The number next to each node is the distance from that node to the square red node as measured by the length of the shortest path. The green edges illustrate one of the two shortest paths between the red square node and the red circle node. The closeness of the red square node is therefore 5/(1+1+1+2+2) = 5/7.
This can be used for example to switch between shortest distance and shortest time or include current traffic information as well as user preferences like avoiding certain types of roads (ferries, highways, ...). In the preprocessing phase, most of the runtime is spent on computing the order in which the nodes are contracted. [3]