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The two nodes adjacent to the core broadcast messages to the rest of the nodes in the fragment. The messages are sent via the branch edge but not via the core. Each broadcast message contains the ID and level of the fragment. At the end of this stage, each node has received the new fragment ID and level.

In this stage, all nodes in the fragment cooperate to find the minimum weight outgoing edge of the fragment. Outgoing edges are edges connecting to other fragments. The messages sent in this stage are in the opposite direction of the broadcast stage. Initialized by all the leaves (the nodes that have only one branch edge), a message is sent through the branch edge. The message contains the minimum weight of the incident outgoing edge it found (or infinity if no such edge was found). The way to find the minimum outgoing edge will be discussed later. For each non-leaf node, given the number of its branch edges as n {\displaystyle n} , after receiving n − − 1 {\displaystyle n-1} convergecast messages, it will pick the minimum weight from the messages and compare it to the weights of its incident outgoing edges. The smallest weight will be sent toward the branch it received the broadcast from.

After the completion of the previous stage, the two nodes connected by the core can inform each other of the best edges they received. Then they can identify the minimum outgoing edge from the entire fragment. A message will be sent from the core to the minimum outgoing edge via a path of branch edges. Finally, a message will be sent out via the chosen outgoing edge to request to combine the two fragments that the edge connects. Depending on the levels of those two fragments, one of two combined operations are performed to form a new fragment; details discussed below.

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