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What’s an MST?

Explore the concept of minimum spanning trees (MST) in connected weighted graphs. Understand what defines an MST, why it matters for minimizing costs in network structures, and common methods to implement MSTs effectively.

A tree that spans the graph

The notion of a spanning tree is defined only for connected graphs. A spanning tree of a connected graph GG is a subgraph in GG that is a tree containing all vertices of GG.

For example, the subgraph of the following graph, highlighted in red, contains all vertices of the graph. It is also a tree since by definition ...