Table 3 (A) Chemical structure of Chloro(methoxy)methane and its labeled molecular scaffold, (B) examples of two-tuple total spatial-(dis)similarity matrices for k = 1 (order) calculated from different (dis-)similarity metrics, (C) example of three-tuple total spatial-(dis)similarity matrix for k = 1 (order) calculated from bond angle ternary measure
(A) 3D molecular structure | ||||||||
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(B) Two-tuple total spatial-(dis)similarity matrices, \( {\mathbb{G}}^{1} \) | ||||||||
\( {\mathbb{G}}^{1} \) based on Euclidean metric | \( {\mathbb{G}}^{1} \) based on Lance-Williams metric | |||||||
C1 | C2 | O3 | Cl4 | C1 | C2 | O3 | Cl4 | |
C1 | 0.000 | 2.408 | 1.439 | 3.939 | 0.000 | 1.000 | 0.973 | 1.000 |
C2 | 2.408 | 0.000 | 1.438 | 1.757 | 1.000 | 0.000 | 0.954 | 0.293 |
O3 | 1.439 | 1.438 | 0.000 | 2.598 | 0.973 | 0.954 | 0.000 | 0.973 |
Cl4 | 3.939 | 1.757 | 2.598 | 0.000 | 1.000 | 0.293 | 0.973 | 0.000 |
\( {\mathbb{G}}^{1} \) based on Soergel metric | \( {\mathbb{G}}^{1} \) based on Angular Separation metric | |||||||
C1 | C2 | O3 | Cl4 | C1 | C2 | O3 | O3 | |
C1 | 0.000 | 1.158 | 1.003 | 1.709 | 0.000 | 1.354 | 0.558 | 1.875 |
C2 | 1.158 | 0.000 | 1.234 | 1.359 | 1.354 | 0.000 | 0.318 | 0.237 |
O3 | 1.003 | 1.234 | 0.000 | 2.235 | 0.558 | 0.318 | 0.000 | 0.952 |
Cl4 | 1.709 | 1.359 | 2.235 | 0.000 | 1.875 | 0.237 | 0.952 | 0.000 |
(C) Three-tuple total spatial-(dis)similarity matrix, \( {{\mathbb{G}}{\mathbb{T}}}^{1} \) | ||||||||
\( {{\mathbb{G}}{\mathbb{T}}}^{1} \) slide 1ij | \( {{\mathbb{G}}{\mathbb{T}}}^{1} \) slide 2ij | |||||||
C1 | C2 | O3 | Cl4 | C1 | C2 | O3 | O3 | |
C1 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.578 | 0.281 |
C2 | 0.000 | 0.000 | 0.578 | 2.470 | 0.000 | 0.000 | 0.000 | 0.000 |
O3 | 0.000 | 1.985 | 0.000 | 2.682 | 1.985 | 0.000 | 0.000 | 0.697 |
Cl4 | 0.000 | 0.390 | 0.163 | 0.000 | 0.390 | 0.000 | 0.553 | 0.000 |
\( {{\mathbb{G}}{\mathbb{T}}}^{1} \) slide 3ij | \( {{\mathbb{G}}{\mathbb{T}}}^{1} \) slide 4ij | |||||||
C1 | 0.000 | 0.578 | 0.000 | 0.297 | 0.000 | 0.281 | 0.297 | 0.000 |
C2 | 0.578 | 0.000 | 0.000 | 1.892 | 2.470 | 0.000 | 1.892 | 0.000 |
O3 | 0.000 | 0.000 | 0.000 | 0.000 | 2.682 | 0.697 | 0.000 | 0.000 |
Cl4 | 0.163 | 0.553 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
