How do minimal tree generators work?

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Minimal tree generators operate by managing two sets of nodes: Remaining Nodes (A) and Visited Nodes (B). The process begins with the minimal edge, defined as the one with the smallest weight, and iterates until no more nodes can be connected. The key criterion for transferring a node from A to B is the minimal edge connecting the two sets. Kruskal's algorithm is mentioned as an alternative approach, which starts with no edges and adds the smallest-weight edge that avoids cycles. Overall, these algorithms are rooted in graph theory and discrete mathematics.
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I was wondering,could someone explain me how do minimal tree generators work?
 
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Is this a Graph Theory or discrete math topic? Is it the minimal tree of the entire graph or connected to some node? mathworld.com

either way its about having 2 sets...the set of Remaining Nodes A and the set of nodes you have visited B. The idea is to move nodes in A to B. The algorithm will always start off with the minimal edge(one with the smallest weight). From there you iterate till no more nodes can be connected to B or A is empty. The criteria for moving a node from A to B is simply the minimal edge that connects A to B.
 
Kruskal's algorithm works differently, starting with no edges and continuing to add the smallest-weight edge that does not form a cycle.
 

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