Table 5 Example of probabilistic transformations on the non-stochastic two-tuple total spatial-(dis)similarity matrix for k = 1, \(_{{\varvec{ns}}} {\mathbb{G}}^{1}\), computed from 3D coordinates of the Chloro(methoxy)methane compound (see Table 1A) by using the Euclidean metric
C1 | C2 | O3 | Cl4 | C1 | C2 | O3 | Cl4 | |
|---|---|---|---|---|---|---|---|---|
Non-stochastic matrix, \(_{ns} {\mathbb{G}}^{1}\) | Simple-stochastic matrix, \(_{ss} {\mathbb{G}}^{1}\) | |||||||
C1 | 0.000 | 2.408 | 1.439 | 3.939 | 0.000 | 0.309 | 0.185 | 0.506 |
C2 | 2.408 | 0.000 | 1.438 | 1.757 | 0.430 | 0.000 | 0.257 | 0.314 |
O3 | 1.439 | 1.438 | 0.000 | 2.598 | 0.263 | 0.263 | 0.000 | 0.475 |
Cl4 | 3.939 | 1.757 | 2.598 | 0.000 | 0.475 | 0.212 | 0.313 | 0.000 |
Double-stochastic matrix, \(_{ds} {\mathbb{G}}^{1}\) | Mutual probability matrix, \(_{mp} {\mathbb{G}}^{1}\) | |||||||
C1 | 0.000 | 0.387 | 0.246 | 0.368 | 0.000 | 0.089 | 0.053 | 0.145 |
C2 | 0.387 | 0.000 | 0.368 | 0.246 | 0.089 | 0.000 | 0.053 | 0.065 |
O3 | 0.246 | 0.368 | 0.000 | 0.387 | 0.053 | 0.053 | 0.000 | 0.096 |
Cl4 | 0.368 | 0.246 | 0.387 | 0.000 | 0.145 | 0.065 | 0.096 | 0.000 |