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TopologicalDescriptors
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tuple of structure.StructureBond
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Inherited from |
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Initializes valid topological descriptors, and creates an empty cached property dictionary.
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Returns all topological descriptor labels as label-key string
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Calculates a set of topological descriptors for a given structure.
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Create descriptor m2io property name for a Descriptor.
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Extracts a single structure if more than one is present.
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Locates the corresponding Descriptor in the class tuple of Descriptors. Looks for Descriptor based on matching the passed string to any of the key, label, or "label (key)" strings.
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Create complete descriptor label-key string
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Evalulates a descriptor for a given structure. If successful, the value is cast to the expected type before returning.
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Returns set of valid descriptor tuples in the form of: (descriptor key, descriptor label, function mapping) @return: set of available topological descriptor mappings @rtype: set of tuples |
Handbook p. 509: First Zagreb index (M_1) -- topological index based on atomic vertex degrees. The first index in strictly related to zero-order connectivity index. Also called the Gutman index.
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Handbook p. 509: First valence Zagreb index (M^v_1) -- topological index based on atomic valence vertex degrees. The first index in strictly related to zero-order connectivity index.
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Handbook p. 509: Second Zagreb index (M_2) -- topological index based on atomic vertex degrees. The second index in strictly related to first-order connectivity index; it is part of the Schuttz molecular topological index.
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Handbook p. 509: Second valence Zagreb index (M^v_2) -- topological index based on atomic valence vertex degrees. The second index in strictly related to first-order connectivity index.
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Handbook p. 114: polarity number (p_2) -- also known as Wiener polarity number; the number of pairs of graph vertices which are separated by three edges. It is usually assumed that the polarity number accounts for the flexibility of acyclic structures, p being equal to the number of bonds around which free rotations can take place.
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Handbook p. 476: simple topological index (S) -- descriptor related to molecular branching, proposed as the product of the vertex degrees for each atom [Narumi, 1987]. NOTE: Take the natural log to avoid overflow.
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Handbook p. 476: harmonic topological index (H) -- descriptor related to the simple topological index [Narumi, 1987].
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Handbook p. 476: geometric topological index (G) -- descriptor related to the simple topological index [Narumi, 1987].
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Handbook p. 86: total structure connectivity index -- connectivity index contemporarily accounting for all the atoms in the graph. This is the square root of the simple topological index proposed by Narumi for measuring molecular branching. (Handbook misprint: inverse square root)
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Handbook p. 9, Wiener operator W(M) -- half the sum of the off-diagonal entries of the matrix M; name taken from the Wiener index. |
Handbook p. 497: Wiener index (W) -- the sum over all bonds of the product of the number of vertices on each side of the bond; ie. the sum of all topological distancesinthe H-depleted molecular graph. Also known as the Weiner number.
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Handbook p. 497: mean Wiener index (W_bar) -- defined from the Wiener index as 2 * W / (A * (A - 1))
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Handbook p. 507: Xu index -- descriptor accounting for molecular size and branching. Defined as sqrt(A) * ln(L), where L represents the valence average topological distance calculated by vertex degree and vertex distance degree of all atoms. NOTE: Use natural log (comparable to E-DRAGON)
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Handbook p. 44: quadratic index (Q) -- obtained by normalization of the first Zagreb index. Also called normalized quadratic index.
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Handbook p. 44: radial centric information index (I^V_C,R) -- defined as the lopping centric information index, but where ng is the number of graph vertices having the same atom eccentricity.
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Handbook p. 113: mean square distance index (MSD) -- calculated from the second order distance distribution moment [Balaban, 1983a]. NOTE: Handbook misprint -- the square root should encompass [A * (A-1)]
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Handbook p. 431: superpendentic index -- calculated from the pendent
matrix, which is a submatrix of the distance matrix which is to the
number of atoms by the number of terminal vertices. The superpendentic
index is calculated as the square root of the sum of the products of
the nonzero row elements in the pendent matrix.
NOTE: As with DRAGON, instead of returning sqrt of sum of ow products:
pow(sum(numpy.prod(pendent_matrix, axis=1)), 0.5)
we avoid overflow by returning the sqrt of sum of log(row products)
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Handbook p. 209: Harary index (H) -- topological index derived from the reciprocal distance matrix by the Wiener operator (Harary number)
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Handbook p. 116: Log of PRS index -- log(Product of Row Sums index) defined as the lof of the product of the vertex distance degrees. Taking the log is preferred due to the large values that can be reached by the PRS index. NOTE: As per Handbook, log is base 10
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Handbook p. 116: Pogliani index (D^nu) -- sum of the ratio of the number of valence electrons to the principal quantum number for each atom.
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Handbook p. 381: Schultz molecular topological index (MTI) -- index derived from the adjacency and distance matrices, defined as the sum over (A+D).v intricacy numbers. NOTE: Handbook decomposes the index into two parts, a sum of square vertex degrees and vertex degree-vertex distance degree products, and erroneously labels the former as "the second Zagreb index". The sum for M2 is over only bonded pair i-j, whereas here is over ALL i-j pairs.
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Handbook p. 381: Schultz molecular topological index (MTI) -- molecular topological index calculated using the vertex degree.
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Handbook p. 382: Schultz molecular topological valence index (MTI^v) -- a vertex-valency-weighted analogue to the Schultz molecular topological index calculated using the valence vertex degree.
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Handbook p. 114: mean distance degree deviation (delta sigma) -- the mean devaiationo f the row sum of the distance matrix from its mean.
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Handbook p. 475: ramification index (r) -- a simple ramification index proposed for acyclic graphs, where the sum runs over all the vertex degrees greater than two.
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Handbook p. 382: Gutman molecular topological index (S_G) -- sum of the topological distance between the vertices vi and vj weighted by the product of the endpoint vertex degrees.
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Handbook p. 382: Gutman molecular topological index (S_G) -- the vertex degree weighted form of S_G.
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Handbook p. 382: Gutman molecular topological valence index (S_G) -- a vertex-valency-weighted analogue of S_G, where the weighting factor is multiplicative.
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Handbook p. 114: average distance degree (sigma^bar) -- average row sum of the distance matrix. Note this is also 2 * (Wiener index) / A.
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Handbook p. 114: unipolarity (simga*) -- minimum value of the vertex distance degrees.
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Handbook p. 114: centralization (delta sigma^*) -- molecular invariant immediately derived from the distance matrix.
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Handbook p. 114: variation (delta sigma^+) -- molecular invariant immediately derived from the distance matrix.
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Adopted from DRAGON: molecular electrotopological variation
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Adopted from DRAGON: maximal electrotopological positive variation
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Adopted from DRAGON: maximal electrotopological negative variation
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Handbook p. 124: eccentric connectivity index (xi^C) -- the sum of the products between eccentricity and vertex degree over all atoms.
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Handbook p. 112: eccentricity (nu) -- sum of atom eccentricities.
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Handbook p. 112: average atom eccentricity (nu^bar) -- average of atom eccentricities.
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Handbook p. 112: eccentricity (Delta nu) -- mean deviation from average of atom eccentricities.
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Handbook p. 85: connectivity indices of mth order -- usually known as Kier-Hall connectivity indices, defined a general scheme based on the Randic index to also calculate zero-order and higher-order descriptors.
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Handbook p. 86: mean valence connectivity indices of mth order -- again, replacing the vertex degree by the valence vertex degree in the similar mean connectivity indices.
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Handbook p. 253: quasi-Wiener index (W^*) -- sum of the reciprocal A - 1 positive eigenvalues was proposed as a molecular descriptor. For acyclic graphs, the quasi-Wiener index coincides with the Wiener index, while for cycle-containing graphs the two descriptors differ. Moreover, it has been demonstrated that the quasi-Wiener index coincides with the Kirchhoff number for any graph.
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Handbook p. 254: first Mohar indices (TI)_1 -- index derived from the Laplacian matrix.
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Handbook p. 254: second Mohar indices (TI)_2 -- index derived from the Laplacian matrix.
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Handbook p. 253: log of spanning tree number (T^*) -- log of the product of the positive A-1 eigenvalues of the Laplacian matrix. NOTE: Take the natural log to avoid overflow.
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Handbook p. 379: benzene-likeliness index -- an aromaticity index based on the first-order valence connectivity index divided by the number of bonds and normalized on the benzene molecule.
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Handbook p. 445: topological charge index (G_k) -- the half-sum of all charge terms corresponding to pair of vertices with topological distance = k and would represent the total charge transfer between atoms placed at topological distance k.
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Handbook p. 445: mean topological charge index (J_k) -- topological charge index divided by the number of edges in an acyclic molecule. Values are set to zero for k greater than the molecular diameter.
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Handbook p. 445: global topological charge index (J) -- sum over mean topological charge indinces, with the superior limit equal to 5. The value was proposed by the authors to obtain uniform length descriptors. NOTE: Past implementation, as well as DRAGON, sum up to k=10
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Handbook p. 118: hyper-distance-path index (D_p) -- defined as applying the Wiener operator to the distance-path matrix, where entry i-j of the matrix is calculated from the distance matrix D as all the possible combinations of two elements taken from d_ij + 1 elements (binomial coefficient).
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Handbook p. 118: reciprocal hyper-distance-pathindex (D_p^-1) -- defined in the same was as the hyper-distance-path index, but where elements of the distance-path matrix are reciprocal.
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Handbook p. 210: square reciprocal distance sum index (Har2) -- the Harary index calculated with the reciprocal squared distance matrix.
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Handbook p. 88: modified Randic index (chi^1_mod) -- sum of atomic properties, accounting for valence electrons and extended connectivities using a Randic connectivity index-type formula. 0.5 * sum_atoms[ sum_atomi_bonds[ Z_i * (delta_i * delta_j) ^ -0.5 ]]
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Handbook p. 42: Balaban centric index (B) -- topological index defined for acyclic graphs based on the pruning of the graph, a stepwise procedure for removing all the terminal vertices.
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Handbook p. 42: lopping centric information index (I_B) -- index defined as the mean information content derived from the pruning of acyclic graphs based on the pruning of the graph, a stepwise procedure for removing all the terminal vertices.
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Handbook p. 475: Kier-Hall electronegativity index (KHE) -- sum of Kier-Hall electrotopological states.
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Adopted from DRAGON: sum of topological distances between all pairs of given atom types.
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Handbook p. 489: index calculated by applying the Wiener operator to the Barysz distance matrix.
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Handbook p. 489: index calculated by applying the Wiener operator to the electronegativities weighted distance matrix.
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Handbook p. 489: index calculated by applying the Wiener operator to the atomic mass weighted distance matrix.
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Handbook p. 489: index calculated by applying the Wiener operator to the van der Waals volume weighted distance matrix.
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Handbook p. 489: index calculated by applying the Wiener operator to the polarizability weighted distance matrix.
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Handbook p. 489: Barysz index (J_het) -- a generalization of the Balaban distance connectivity index calculated by applying the Ivanciuc-Balaban operator to the Barysz distance matrix.
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Handbook p. 489: index calculated by applying the Ivanciuc-Balaban operator to the electronegativities weighted distance matrix.
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Handbook p. 489: index calculated by applying the Ivanciuc-Balaban operator to the atomic mass weighted distance matrix.
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Handbook p. 489: index calculated by applying the Ivanciuc-Balaban operator to the van der Waals volume weighted distance matrix.
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Handbook p. 489: index calculated by applying the Ivanciuc-Balaban operator to the polarizability weighted distance matrix.
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Handbook p. 112: topological diameter (D) -- defined as the maximum atom eccentricity
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Handbook p. 112: topological radius (R) -- defined as the minimum atom eccentricity
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Handbook p. 390: Petitjean shape index (I_2) -- a topological anisometry descriptor, also called a graph-theoretical shape coefficient.
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Handbook p. 21: Balaban distance connectivity index (J) -- defined in
terms of sums over each i th row of the distance matrix as:
B/(C+1) * sum_bonds[ (vertex dist_i * vertex dist_j) ^ -0.5 ]
It is also called distance connectivity index or average distance sum
connectivity.
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Handbook p. 88: solvation connectivity indices (m chi^s_q) -- descriptor defined in order to model solvation entropy and describe dispersion interactions in solution.
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Handbook p. 85: connectivity indices of mth order -- usually known as Kier-Hall connectivity indices, defined a general scheme based on the Randic index to also calculate zero-order and higher-order descriptors.
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Handbook p. 85: mean connectivity indices of mth order -- the Handbook only describes the mean Randic connectivity index (m=1), defined as the Randic connectivity index divided by the number of bonds. Here, we extrapolate to zero and higher orders
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Handbook p. 116: RDCHI index -- topological index based on a Randic-type formula, which increases with molecular size but decreases with molecular branching.
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Handbook p. 116: RDSQ index -- topological index based on a Randic-type formula, which increases with both molecular size and molecular branching.
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Handbook p. 249: Kier alpha-modified shape descriptor (m kappa_alpha) -- descriptor defined in terms of the number of graph vertices A and the number of paths with length (m = 1,2,3). The alpha-modified version takes into account the different shape contribution of heteroatoms and hybridization states.
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Handbook p. 178: Kier molecular flexibility index (fi) -- a measure of molecular flexibility derived from the Kier alpha-modified shape descriptors, kappa1 encodes information about the count of atoms and relative cyclicity of molecules, while kappa2 encodes information about branching or relative spatial density of molecules.
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Handbook p. 393: Molecular path/walk indices -- the average sum of atomic path/walk indices of equal length. Obtained by separately summing all the paths and walks of the same length, and then calculating the ratio between their counts.
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Molecular Descriptors p. 42: E-state topological parameter (TI^E) -- derived by applying the Ivanciuc-Balaban operator to the E-state index values. It has to be pointed out that the proposed formula for the E-state topological parameter cannot be used for every molecule because it presents two drawbacks: (1) it cannot be calculated when there exists one atom in the molecule with negative E-state value; (2) it assumes very large values even when one S value tends to zero. To overcome these drawbacks of the original formula, an alternative formula (adopted in the DRAGON descriptors) is used here.
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Unknown source: number of chiral atoms -- count chiral atoms labeled with either R or S (ignoring ANR and ANS).
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Adopted from DRAGON: number of rings of heavy atom count n
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Handbook p. 16: atom number (A) -- defined as the total number of atoms in a molecule, which refers only to non-hydrogen atoms (atom count).
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Handbook p. 28: bond number (B) -- defined as the number of bonds in the molecule (edge counting; bond count).
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Molecular Descriptors p. 655: (A_R) -- the total number of atoms belonging to rings
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Molecular Descriptors p. 655: (B_R) -- the total number of bonds belonging to rings
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Molecular Descriptors p. 655: number of ring systems (NRS)
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Molecular Descriptors p. 655: normalized number of ring systems (NRS*) by the cyclomatic number.
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Molecular Descriptors p. 655: ring fusion degree (RFD) -- the reciprocal of the normalized number of ring systems.
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Molecular Descriptors p. 656: total ring size (R) -- the sum of the ring size of all the single cycles of all the ring systems; in this case, the atoms belonging to fused connections are counted twice.
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Molecular Descriptors p. 656: ring perimeter (R_P) -- represents the perimeter of all the rings present in the molecule.
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Molecular Descriptors p. 656: ring bridges (R_B) -- represents the number of bridge edges.
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Molecular Descriptors p. 656: molecular cyclized degree (MCD) -- ratio of ring atoms to total atoms.
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Molecular Descriptors p. 656: ring fusion density (RF Delta)
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Molecular Descriptors p. 656: ring complexity index (C_R)
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Molecular Descriptors p. 609: Total VSA for all atoms
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Molecular Descriptors p. 611: P_VSA based on molar refractivity. Property interval boundaries extracted from Table P16, p. 611
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Molecular Descriptors p. 611: P_VSA based on log P values, to capture hydrophobic and hydrophillic effect. Property interval boundaries extracted from Table P16, p. 611
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Molecular Descriptors p. 611: P_VSA based on Gasteiger charges, ie. partial equalization of orbital electronegativity (PEOE). Property interval boundaries extracted from Table P16, p. 611
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Handbook p. 313: Hydrogen-depleted molecule.
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Fully hydrogenated molecule.
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Handbook p. 474: (h_i) -- the number of hydrogen atoms bonded to a given heavy atom.
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Returns list of atom indices, which are 1-based.
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Returns list of all pairs of atom indices, which are 1-based.
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Returns list of bond index tuples, which are 1-based. Sorts indices (for comparision purposes), and ignores zero-order bonds.
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Handbook p. 2: adjacency matrix (A) -- represents the whole set of connections between adjacent pairs of atoms. The entries a_ij of the matrix equal one if vertices vi and vj are bonded, and zero otherwise. The adjacency matrix is symmetric with dimension A x A , where A is the number of atoms and it is derived from an H-depleted molecular graph.
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Handbook p. 474, 2: vertex degree (delta_i) -- the ith row sum of the adjacency matrix.
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Handbook p. 474: valence vertex degree (delta^v_i) -- vertex degree taking into account all valence electrons of the ith atom. A simplified version of the equation below.
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Handbook p. 474: valence vertex degree (delta^v_i) -- vertex degree taking into account all valence electrons of the ith atom. It encodes the electronic identity of the atom in terms of both valence electron and core electron counts. Given as: (Z^v_i - h_i) / (Z_i - Z^v_i - 1) For atoms of higher principal quantum levels (P, S, Cl, Br, I), Kier and Hall proposed to account for both valence and nonvalence electrons Z^v_i = number of valence electrons of ith atom h_i = number of hydrogens bonded to atom Z_i = total number of electrons of ith atom (atomic number)
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Returns the shortest path from atom index1 to atom index2, inclusive.
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Handbook p. 112: distance matrix (D) -- matrix of all topological distances between all the atom pairs. Also known as the vertex distance matrix. The topological distance d_ij the number of edges in the shortest path between the vertices vi and vi; the off-diagonal entries of the distance matrix equal one if vertices vi and v, are adjacent (i.e. the atoms i and j are bonded) and are greater than one otherwise. The diagonal elements are of course equal to zero. The distance matrix is symmetric with dimension A x A, where A is the number of atoms, and is derived from the H-depleted molecular graph.
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Handbook p. 112: reciprocal distance matrix (D^-1) -- a square symmetric A x A matrix derived from the distance matrix where each off-diagonal element is the reciprocal of the topological distance d between the considered vertices (and 0 for d_ii).
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Handbook p. 112: reciprocal square distance matrix (D^-2) -- a square symmetric A x A matrix derived from the distance matrix where each off-diagonal element is the reciprocal of the topological distance d between the considered vertices (and 0 for d_ii).
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Handbook p. 113, vertex distance degree (sigma_i) -- the ith row sum of the distance matrix. Also known as the distance number, distance index, distance rank, vertex distance sum, or distance of a vertex.
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Handbook p. 112, atom eccentricity (nu_i) -- maximum value entry in the ith row of the distance matrix, i.e. the maximum distance from theith vertex to any other vertices (vertex eccentricity).
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Handbook p. 113, graph distance count (f^k) -- total number of distances in the graph equal to k
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Handbook p. 116: reciprocal distance sum (RDS_i) -- sum of the reciprocal distance matrix elements in the ith row.
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Handbook p. 85, all shortest paths keyed by path lengths. The paths are equivalent to mth order subgraphs in the molecular structure.
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Handbook p. 94, cyclomatic number -- the number of independent cycles (or rings), and, more exactly, the number of non-overlapping cycles. Should be equivalent to len(st.ring)
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Handbook p. 159: intrinsic state (I_i) -- calculated from the principal
quantum number, the number of valence electrons, and the number of
sigma electrons of the ith atom in the H-depleted molecular graph.
NOTE: Molecular Descriptors p. 284, Table E11 and DRAGON use the simple valence
vertex degree when calculating the instrisic state.
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Handbook p. 159: field effect (Delta I_i) -- calculated as perturbation of the intrinsic state of ith atom by all other atoms in the molecule. The exponent k is a parameter to modify the influence of distant or nearby atoms for particular studies. Usually it is taken as k = 2.
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Handbook p. 253: laplacian eigenvalues (lambda_i) -- from the Laplacian matrix, defined as the difference between the vertex degree matrix and the adjacency matrix. The diagonalization of the Laplacian matrix gives A real eigenvalues hi which constitute the Laplacian spectrum. All eignevalues are (a) non-negative numbers, (b) the last value is always zero, and (c) the second to last is great than zero if the graph is connected.
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Handbook p. 445: charge term matrix (CT) -- an unsymmetric matrix of charge terms that are graph invariants related to the charge transfer between the pair of considered vertices. The diagonal entries of the CT matrix represent the topological valence of the atoms; the off-diagonal entries CT_ij represent a measure of the net charge transferred from the atom j to the atom i.
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Collects all bonds in the heavy atom structure that are aromatic.
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Handbook p. 28: conventional bond order (sigma^*) -- within the framework of the graph theory, specifically the multigraph, this is defined as being equal to 1, 2, 3, and 1.5 for single, double, triple and aromatic bonds, respectively.
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Handbook p. 488: multigraph distance matrix (*D) -- a weighted distance matrix where the distance from vertex vi to vertex vj is obtained by counting the edges in the shortest path between them, where each edge counts as the inverse of the conventional bond order, i.e. the relative topological distance, and therefore contributes 1 / bond order to the overall path length.
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Handbook p. 488: Barysz distance matrix (D^Z) -- a weighted distance matrix accounting simultaneously for the presence of heteroatoms and multiple bonds in the molecule.
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Molecular Descriptors p. 909: generalized Ivanciuc weighting from the Barysz distance matrix with Sanderson electronegativities See: Handbook p. 488, Barysz distance matrix
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Molecular Descriptors p. 909: generalized Ivanciuc weighting from the Barysz distance matrix with atomic masses See: Handbook p. 488, Barysz distance matrix
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Molecular Descriptors p. 909: generalized Ivanciuc weighting from the Barysz distance matrix with van der Waals volumes See: Handbook p. 488, Barysz distance matrix
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Molecular Descriptors p. 909: generalized Ivanciuc weighting from the Barysz distance matrix with polarizabilities See: Handbook p. 488, Barysz distance matrix
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Handbook p. 480: atomic walk count (awc) -- the total number of equipoise walks of length k starting from vertex vi.
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Molecular Descriptors p. 609: van der Waals surface area (VSA) -- calculated from the atomic van der Waals radius, summing over contributions from atoms in the adjacency matrix.
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Handbook p. 7, Ivanciuc-Balaban operator IB(M) -- a modified Randic
operator summing over all bonded pairs for row sums of each participant:
B/(C+1) * sum_bonds[ (R(i) * R(j)) ^ -0.5 ]
C is the cyclomatic number, B is the number of bonds, and R is the row
sum operator.
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Calculates atom centric index based on an atomic property function and a base function of the centric index sum.
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Handbook p. 86: formula for generalized connectivity indices, used for several descriptors.
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Molecular Descriptors p. 609: P_VSA -- the amount of van der Waals surface area (VSA) having a property value in a certain range. These descriptors correspond to a partition of the molecular surface area conditioned by the atomic values of the property P.
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