A connected, undirected, edge-weighted graph that connects all vertices together without cycles with the minimum possible total edge weight.
As long as all the edge lengths are positive, this will always form a Tree, hence the name.
Example
12 is the minimum weight subset of edges that span the shown graph.
Input: An undirected and connected graph G = (V,E) with edge lengths l_e
Output: A tree T = (V, E') with E' being a subset of E that minimizes:
length(T)=sum(l_e) for all e in E'