In a weighted graph, edges have an associated number called weight, which might represent distances, costs times, or other quantities. The minimum spanning tree in a weighted graph minimizes the total weights of the edges necessary to connect all the vertices. Graphs can represent many real-world entities, including airline routes, electrical circuits, and job scheduling. The adjacency matrix can be used to represent a graph's edges in a computer program. Topological sorting is useful for scheduling projects which contain many tasks contingent on other tasks. There may be many correct topological sorts for a given graph. You can create a topological sort of a graph that contains cycles.

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Polynomial Time

The problems for which the deterministic polynomial-time algorithm exists belong to the complexity class (p) and it is central in the field of computational complexity theory. According to Cobham’s thesis, polynomial time is a synonym for “feasible”, “fast”, and “efficient”.