Date of this Version
Stein's Method and Applications
Two methods are used to compute the expected value of the length of the minimal spanning tree (MST) of a graph whose edges are assigned lengths which are independent and uniformly distributed. The first method yields an exact formula in terms of the Tutte polynomial. As an illustration, the expected length of the MST of the Petersen graph is found to be 34877/12012 = 2.9035 .... A second, more elementary, method for computing the expected length of the MST is then derived by conditioning on the length of the shortest edge. Both methods in principle apply to any finite graph. To illustrate the method we compute the expected lengths of the MSTs for complete graphs.
Preprint of an article submitted for consideration in Stein's Method and Applications © 2005 World Scientific Publishing Company.
Fill, J. A., & Steele, J. M. (2005). Exact Expectations of Minimal Spanning Trees for Graphs With Random Edge Weights. Stein's Method and Applications, 1-10. Retrieved from https://repository.upenn.edu/statistics_papers/17
Date Posted: 27 November 2017
This document has been peer reviewed.