A minimum spanning tree would be one with the lowest total cost.

This can be achieved by using the Spanning tree protocol.

A number of problems from graph theory are called Minimum spanning tree.

A mesh is made by folks like me, then bridges find a spanning tree.

A single graph can have many different spanning trees.

Depending on what the graph looks like, there may be more than one minimum spanning tree.

In the second step, a maximal-weight spanning tree is searched for.

Note that, the spanning tree is not unique and it depends on the order of messages in the system.

If each edge has a distinct weight then there will be only one, unique minimum spanning tree.

Research has also considered parallel algorithms for the minimum spanning tree problem.

First, it is proved that the algorithm produces a spanning tree.

But only a connected graph has a spanning tree.

They were used to achieve the best complexity to date for finding a minimum spanning tree.

In directed graphs, the maximum spanning tree solution cannot be used.

Regarding the spanning tree algorithm, I would also add a couple of clarifying points.

Prim's purpose is to find a minimum spanning tree for a graph.

Basically the fundamental set of loops can be found by constructing spanning tree for the network.

The method relies on identifying spanning trees that are common to both graphs.

The "bridge" and "spanning tree" concepts described above do not scale to large international networks.

For any given spanning tree these cycles form a basis for the cycle space.

Because of this, maze generation is often approached as generating a random spanning tree.

If the graph is connected, the forest has a single component and forms a minimum spanning tree.

Minimal spanning trees have applications to the construction and pricing of communication networks.

Only ever gone down a few times at like 2am in the morning due to what looked like a spanning tree misconfiguration.

This is similar to the minimum spanning tree problem which concerns undirected graphs.