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A longest path between two given vertices s and t in a weighted graph G is the same thing as a shortest path in a graph −G derived from G by changing every weight to its negation. Therefore, if shortest paths can be found in −G, then longest paths can also be found in G. [4]
The items separated by the longest minimal chains in the encyclopedia (especially where these are more than four links long). The shortest known chain between the two items should be specified. Generalisation over time, where possible, seems to produce the shortest chains. Failing this, try generalisation over space to reduce chain length.
Average path length, or average shortest path length is a concept in network topology that is defined as the average number of steps along the shortest paths for all possible pairs of network nodes. It is a measure of the efficiency of information or mass transport on a network.
This is one way of looking at the small world problem. An alternative view of the problem is to imagine the population as a social network and attempt to find the average path length between any two nodes. Milgram's experiment was designed to measure these path lengths by developing a procedure to count the number of ties between any two people.
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Dijkstra's algorithm can be used to find the shortest path between two articles in Wikipedia. There will be two articles connected by a shortest path which is longer than any other shortest path between any of the other articles in Wikipedia. 82.136.254.117 wondered what those two articles are. I think this is a non-trivial problem.
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An analogy would be a person walking across a room; rather than examining every possible route in advance, the person would generally walk in the direction of the destination and only deviate from the path to avoid an obstruction, and make deviations as minor as possible. Two primary problems of pathfinding are (1) to find a path between two ...