ChemInform Abstract: Eigenvalues as Molecular Descriptors

Randić, Milan; Vrac̆ko, Marjan; Novič, Marjana

doi:10.1002/chin.200130292

Cited by 13 publications

(15 citation statements)

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“…Clearly, this result demonstrates that certain measures/functions based on the eigenvalues of graphs possess a high discrimination power. This contradicts the widely assumed hypothesis that graph spectra are not feasible to discriminate graphs properly because of the existence of isospectral graphs, see [34], [35]. Another positive example can be found in [36] where Dehmer et al presented spectrum-based measures based on a probability distribution of structural values with low degeneracy.…”

Section: Methods and Resultsmentioning

confidence: 98%

Structural Discrimination of Networks by Using Distance, Degree and Eigenvalue-Based Measures

2012

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In chemistry and computational biology, structural graph descriptors have been proven essential for characterizing the structure of chemical and biological networks. It has also been demonstrated that they are useful to derive empirical models for structure-oriented drug design. However, from a more general (complex network-oriented) point of view, investigating mathematical properties of structural descriptors, such as their uniqueness and structural interpretation, is also important for an in-depth understanding of the underlying methods. In this paper, we emphasize the evaluation of the uniqueness of distance, degree and eigenvalue-based measures. Among these are measures that have been recently investigated extensively. We report numerical results using chemical and exhaustively generated graphs and also investigate correlations between the measures.

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Section: Methods and Resultsmentioning

confidence: 98%

Structural Discrimination of Networks by Using Distance, Degree and Eigenvalue-Based Measures

2012

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“…The existence of cospectral graphs justifies the general observation that eigenvalue-based graph invariants are not effective in distinguishing non-isomorphic graphs. However, this result suggests the contrary for several classes of graphs [48,49].…”

Section: Non-parametric Graph Entropiesmentioning

confidence: 83%

Entropy and the Complexity of Graphs Revisited

Mowshowitz

Dehmer

2012

Entropy

190

129

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This paper presents a taxonomy and overview of approaches to the measurement of graph and network complexity. The taxonomy distinguishes between deterministic (e.g., Kolmogorov complexity) and probabilistic approaches with a view to placing entropy-based probabilistic measurement in context. Entropy-based measurement is the main focus of the paper. Relationships between the different entropy functions used to measure complexity are examined; and intrinsic (e.g., classical measures) and extrinsic (e.g., Körner entropy) variants of entropy-based models are discussed in some detail.

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“…At that time one of the authors (MR) too was visiting Basak and attending the seminar where Nandy also presented the DNA plot of the complete human b-globin gene, part of which is illustrated in Figure 1. The distance/distance (D/D) matrices [44,45] , which were introduced into chemical graph theory half a dozen years ago to characterize the degree of bending of chain-like molecules, can be used for the numerical characterization of graphical representations of DNA, even though the DNA graphical representation is not a path graph, but a path over the Cartesian coordinate system. By numerical characterization, the construction of a set of invariants of graphical objects is understood, not a single number or a pair of numbers.…”

Section: Milestones In Graphical Bioinformaticsmentioning

confidence: 99%

“…Table 19 suggests that amino acid pairs having differences of 12 and 0 can be ignored, as they represent individual (chance) alignments at great separations. Thus there are a short segment with the difference of 21, a sizable segment (24,23), (25,24), (30,29), (31,30), (32,31), (33,32), (34,33), (35,34), (36,35), (39,38), (42,41), (44,43), (45,44), (46,45), (47, 46), (48,47), (49,48), (50,49), (51,50), (52,51), (55,54), (56,55), (59,58), (60,59), (61,60), …”

Section: Exact Solution To the Protein Alignment Problemmentioning

confidence: 99%

Milestones in graphical bioinformatics

Randić

Novič

Plavšić

2013

Int J of Quantum Chemistry

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After reviewing the field of graphical bioinformatics, we have selected two dozen of the most significant publications that represent milestones of graphical bioinformatics. These publications can be viewed as forming the backbone of graphical bioinformatics, the branch of bioinformatics that initiates analysis of DNA, RNA, and proteins by considering various graphical representations of these sequences. Graphical bioinformatics, a division of bioinformatics that analyzes sequences of DNA, RNA, proteins, and proteomics maps by developing and using tools of discrete mathematics and graph theory in particular, has expanded since the year 2000, although pioneering contributions date back to Hamory (1983) and Jeffrey (1990). We chronologically follow the development of graphical bioinformatics, without assuming that readers are familiar with discrete mathematics or graph theory. Readers unfamiliar with graph theory may even have some advantage over those who have been only superficially exposed to graph theory, inview of wide misconceptions and misinformation about chemical graph theory among quantum chemists, physical chemists, and medicinal chemists in past decades. © 2013 Wiley Periodicals, Inc.

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ChemInform Abstract: Eigenvalues as Molecular Descriptors

Cited by 13 publications

References 0 publications

Structural Discrimination of Networks by Using Distance, Degree and Eigenvalue-Based Measures

Structural Discrimination of Networks by Using Distance, Degree and Eigenvalue-Based Measures

Entropy and the Complexity of Graphs Revisited

Milestones in graphical bioinformatics

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