Minimum Spanning Tree Approach Research Articles

Minimal spanning tree approach to percolation and conductivity threshold

The minimal spanning tree (MST) method to analyse order and disorder in distributions of objects is used to investigate the percolation transition on a triangular lattice. It is shown numerically that the value of the threshold probability is retrieved, simultaneously with a new geometrical parameter: the mean edge length. This is expected to be useful in the conductivity studies of percolation networks such as dielectric breakdown, conductivity and other propagation phenomena. The potentialities of the method in dealing with an extensive study of percolation on continuous as well as lattice systems are also exhibited.

Application of pattern recognition to structure-activity problems: Use of minimal spanning tree

A graph-theoretical algorithm based on the minimal spanning tree (MST) is applied to structure—activity problems. The method is helpful in interpreting the results of cluster analysis, and becomes useful by combining with the mapping method that illustrates approximations of a multidimensional data structure. The antibacterial spectra of cephalosporins are analyzed by the MST approach and a linear mapping method. The main diameter obtained by MST gives the representative data set and clarifies the substituent effect on the antibacterial spectra. Relations between the central nervous system activity of benzodiazepine derivatives and their physicochemical parameters are also analyzed by MST and nonlinear mapping methods. These results for cephalosporins and benzodiazepines prove that MST is very useful in understanding the position of compounds in feature space and their activities.