The phrase "a random spanning tree" is correct and usable in written English.
It can be used in contexts related to graph theory, computer science, or network design when discussing a specific type of tree structure that connects all vertices in a graph without cycles and is chosen randomly.
Example: "In our analysis, we generated a random spanning tree to evaluate the efficiency of the network routing algorithm."
Alternatives: "a stochastic spanning tree" or "a probabilistic spanning tree".
The random spanning tree is generated by starting from a randomly picked SNP and growing edges that connect the remaining SNPs in a random order.
The different models are Erdös-Rényi, Random spanning trees (several random spanning trees are selected in each cluster to match the required density) and Geometric random selection in a 3D Euclidean space [Geo3D Przulj et al. (2004)] adapting the distance threshold to the desired cluster density.
The three methods were applied to random graphs of different edge densities simulated according to several models: Erdös-Rényi, Random spanning trees and Geometric random graphs [Geo3D, Przulj et al. (2004)] (see Section 2).
All the ontologies are randomly generated by constructing a minimal spanning tree from a random matrix.
The proposed algorithm can guarantee the connectivity of the generated random graph through forming a spanning tree; the number of lines in the generated random graph is completely determined by the required average degree; the node degree distribution fits well with real-world power grid topologies; and the number of connected components in the generated random graph is controllable.
As a result we obtain a spanning tree of K ≤ n.
A spanning tree (or a forest of spanning trees) can be computed for any graph.
Thus, the number of lines to be expanded S is S = langle krangle cdot n/2 - (n - 1) (9)In this way, the process of generating a connected random graph can be divided into two stages: randomly generating a spanning tree with n nodes and expanding the spanning tree by randomly adding a certain number of lines.
In the first stage, a spanning tree with a given number of nodes is randomly constructed; in the second stage, the spanning tree is expanded to the required random graph by arbitrarily adding a certain number of lines to it.
