Returns the tree corresponding to the given Prüfer sequence.
A Prüfer sequence is a list of n - 2 numbers between 0 and n - 1, inclusive. The tree corresponding to a given Prüfer sequence can be recovered by repeatedly joining a node in the sequence with a node with the smallest potential degree according to the sequence.
sequence (list) – A Prüfer sequence, which is a list of n - 2 integers between zero and n - 1, inclusive.
The tree corresponding to the given Prüfer sequence.
- Return type
There is a bijection from labeled trees to Prüfer sequences. This function is the inverse of the
Sometimes Prüfer sequences use nodes labeled from 1 to n instead of from 0 to n - 1. This function requires nodes to be labeled in the latter form. You can use
networkx.relabel_nodes()to relabel the nodes of your tree to the appropriate format.
This implementation is from 1 and has a running time of \(O(n)\).
Wang, Xiaodong, Lei Wang, and Yingjie Wu. “An optimal algorithm for Prufer codes.” Journal of Software Engineering and Applications 2.02 (2009): 111. <https://doi.org/10.4236/jsea.2009.22016>
There is a bijection between Prüfer sequences and labeled trees, so this function is the inverse of the
>>> edges = [(0, 3), (1, 3), (2, 3), (3, 4), (4, 5)] >>> tree = nx.Graph(edges) >>> sequence = nx.to_prufer_sequence(tree) >>> sequence [3, 3, 3, 4] >>> tree2 = nx.from_prufer_sequence(sequence) >>> list(tree2.edges()) == edges True