Use of path matrices for a characterization
                    of molecular structures

Randić, Milan; Guo, Xiao-Feng; Bobst, Sol

doi:10.1090/dimacs/051/23

Cited by 10 publications

(11 citation statements)

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“…In Table 1, we have listed a dozen matrices of interest in chemistry 3–19. In a recent book on graph theoretical matrices in chemistry,20 one can find more on matrices of Chemical Graph Theory.…”

Section: Matrices Of Interest In Structure‐property‐activity Studiesmentioning

confidence: 99%

“…Path graphs13, 14 and graphical matrices13, 37, 38 represent a novel class of matrices in which matrix elements are not numbers but subgraphs. Colloquially, one may refer to invariants derived from graphical matrices as “dual invariants,” because one has two steps in selecting invariants: (1) one decides how is a subgraph representing the element ( i, j ) selected; and (2) one is at liberty to select one of numerous subgraphs invariants to represent the subgraphs selected.…”

Section: Matrices Of Interest In Structure‐property‐activity Studiesmentioning

confidence: 99%

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Novel graph distance matrix

et al. 2010

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We have introduced novel distance matrix for graphs, which is based on interpretation of columns of the adjacency matrix of a graph as a set of points in n-dimensional space, n being the number of vertices in the graph. Numerical values for the distances are based on the Euclidean distance between n points in n-dimensional space. In this way, we have combined the traditional representation of graphs (drawn as 2D object of no fixed geometry) with their representation in n-dimensional space, defined by a set of n-points that lead to a representation of definite geometry. The novel distance matrix, referred to as natural distance matrix, shows some structural properties and offers novel graph invariants as molecular descriptors for structure-property-activity studies. One of the novel graph descriptors is the modified connectivity index in which the bond contribution for (m, n) bond-type is given by 1/ radical(m + n), where m and n are the valence of the end vertices of the bond. The novel distance matrix (ND) can be reduced to sparse distance-adjacency matrix (DA), which can be viewed as specially weighted adjacency matrix of a graph. The quotient of the leading eigenvalues of novel distance-adjacency matrix and novel distance matrix, as illustrated on a collection of graphs of chemical interest, show parallelism with a simple measure of graph density, based on the quotient of the number of edges in a graph and the maximal possible number of edges for graphs of the same size.

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Section: Matrices Of Interest In Structure‐property‐activity Studiesmentioning

confidence: 99%

Section: Matrices Of Interest In Structure‐property‐activity Studiesmentioning

confidence: 99%

Novel graph distance matrix

et al. 2010

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“…In the case of trees Lovasz and Pelikan [42] have interpreted the leading eigenvalue of the adjacency matrix of graphs as an index of ''branching'' of graphs. More recently it was suggested that the leading eigenvalue of a graphical matrix in which matrix element (i, j) is the leading eigenvalues of the path between vertices i and j may be even a better index of branching of skeletal graphs [43,44].…”

Section: Matrix Invariantsmentioning

confidence: 99%

On representation of proteins by star-like graphs

Randić

Zupan

Vikić‐Topić

2007

Journal of Molecular Graphics and Modelling

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“…For acyclic molecules of a similar size (e.g. isomers) W is an indicator of the degree of molecular branching. − However, this interpretation has limitations and better alternative characterization of branching not based on the Wiener number was considered since. − …”

Section: Average X−y Base Distancementioning

confidence: 99%

“…In another study Randić, Vračko, and Novič related the leading eigenvalue of the line adjacency matrix of an embedded graph as a measure of molecular flexibility. More recently, the leading eigenvalue of the path matrix was found to offer an even better, or at least more discriminatory, characterization of molecular branching. , The leading eigenvalue of the D/DD matrix (the elements of which are constructed as the quotient of the corresponding elements of the distance matrix (D) and the detour matrix (DD)) ,− was suggested as a measure of molecular cyclicity. , In view of the apparent structural significance of the leading eigenvalues of various matrices associated with chemical structures it seems worthwhile to explore the use of the leading eigenvalues of condensed DNA matrices for the characterization of DNA. In passing we should add that other eigenvalues, even eigenvectors, have been considered as a source for construction of topological indices …”

Section: Invariants Of Reduced Matricesmentioning

confidence: 99%

Characterization of DNA Primary Sequences Based on the Average Distances between Bases

Randić

Basak

2001

J. Chem. Inf. Comput. Sci.

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We outline numerical characterization of DNA primary sequence based on calculation of the average distance between pairs of nucleic acid bases. This leads to a representation of DNA by a condensed 4 x 4 symmetrical matrix, the elements of which give the average separation between pair of bases X, Y in DNA (X, Y = A, C, G, T). As an invariant of choice we consider the leading eigenvalue of the derived 4 x 4 matrix. Additional structurally related invariants were obtained by constructing additional "higher order" 4 x 4 matrices derived from the initial 4 x 4 matrix by raising its elements to higher powers. Suitably normalized leading eigenvalue of these matrices offer a novel characterization of DNA primary sequences, referred to as "DNA profiles". The approach is illustrated on exon 1 of human beta-globin gene.

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Use of path matrices for a characterization of molecular structures

Cited by 10 publications

References 0 publications

Novel graph distance matrix

Novel graph distance matrix

On representation of proteins by star-like graphs

Characterization of DNA Primary Sequences Based on the Average Distances between Bases

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