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40
INEQUALITIES
, 2009
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EmmertStreib F: On entropybased molecular descriptors: statistical analysis of real and synthetic chemical structures
 J Chem Inf Model
"... This paper presents an analysis of entropybased molecular descriptors. Specifically, we use real chemical structures, as well as synthetic isomeric structures, and investigate properties of and among descriptors with respect to the used data set by a statistical analysis. Our numerical results prov ..."
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Cited by 11 (8 self)
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This paper presents an analysis of entropybased molecular descriptors. Specifically, we use real chemical structures, as well as synthetic isomeric structures, and investigate properties of and among descriptors with respect to the used data set by a statistical analysis. Our numerical results provide evidence that synthetic chemical structures are notably different to real chemical structures and, hence, should not be used to investigate molecular descriptors. Instead, an analysis based on real chemical structures is favorable. Further, we find strong hints that molecular descriptors can be partitioned into distinct classes capturing complementary information.
MOLecular Structure GENeration with MOLGEN, new features and future developments
 Fresenius J. Anal. Chem
, 1997
"... MOLGEN is a computer program system which is designed for generating molecular graphs fast, redundancy free and exhaustively. In the present paper we describe its basic features, new features of the current release MOLGEN 3.5, and future developments which provide considerable improvements and ex ..."
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MOLGEN is a computer program system which is designed for generating molecular graphs fast, redundancy free and exhaustively. In the present paper we describe its basic features, new features of the current release MOLGEN 3.5, and future developments which provide considerable improvements and extensions. 1 Introduction MOLGEN [17] is a generator for molecular graphs (=connectivity isomers or constitutional formulae) allowing to generate all isomers that correspond to a given molecular formula and (optional) further conditions like prescribed and forbidden substructures, ring sizes etc. The input consists of ffl the empirical formula, together with ffl an optional list of macroatoms, which means prescribed substructures that must not overlap, ffl an optional goodlist, that consists of prescribed substructures which may overlap, ffl an optional badlist, containing forbidden substructures, ffl an optional interval for the minimal and maximal size of rings, ffl an optional num...
Information Indices with High Discriminative Power for Graphs
, 2011
"... In this paper, we evaluate the uniqueness of several informationtheoretic measures for graphs based on socalled information functionals and compare the results with other information indices and noninformationtheoretic measures such as the wellknown Balaban J index. We show that, by employing a ..."
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In this paper, we evaluate the uniqueness of several informationtheoretic measures for graphs based on socalled information functionals and compare the results with other information indices and noninformationtheoretic measures such as the wellknown Balaban J index. We show that, by employing an information functional based on degreedegree associations, the resulting information index outperforms the Balaban J index tremendously. These results have been obtained by using nearly 12 million exhaustively generated, nonisomorphic and unweighted graphs. Also, we obtain deeper insights on these and other topological descriptors when exploring their uniqueness by using exhaustively generated sets of alkane trees representing connected and acyclic graphs in which the degree of a vertex is at most four.
ENTROPY BOUNDS FOR HIERARCHICAL MOLECULAR NETWORKS
, 2008
"... In this paper we derive entropy bounds for hierarchical networks. More precisely, starting from a recently introduced measure to determine the topological entropy of nonhierarchical networks, we provide bounds for estimating the entropy of hierarchical graphs. Apart from bounds to estimate the en ..."
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In this paper we derive entropy bounds for hierarchical networks. More precisely, starting from a recently introduced measure to determine the topological entropy of nonhierarchical networks, we provide bounds for estimating the entropy of hierarchical graphs. Apart from bounds to estimate the entropy of a single hierarchical graph, we see that the derived bounds can also be used for characterizing graph classes. Our contribution is an important extension to previous results about the entropy of nonhierarchical networks because for practical applications hierarchical networks are playing an important role in chemistry and biology. In addition to the derivation of the entropy bounds, we provide a numerical analysis for two special graph classes, rooted trees and generalized trees, and demonstrate hereby not only the computational feasibility of our method but also learn about its characteristics and interpretability with respect to data analysis.
Dehmer M: Integrative Network Biology: Graph Prototyping for CoExpression Cancer Networks
 PLoS ONE
"... Networkbased analysis has been proven useful in biologicallyoriented areas, e.g., to explore the dynamics and complexity of biological networks. Investigating a set of networks allows deriving general knowledge about the underlying topological and functional properties. The integrative analysis of ..."
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Networkbased analysis has been proven useful in biologicallyoriented areas, e.g., to explore the dynamics and complexity of biological networks. Investigating a set of networks allows deriving general knowledge about the underlying topological and functional properties. The integrative analysis of networks typically combines networks from different studies that investigate the same or similar research questions. In order to perform an integrative analysis it is often necessary to compare the properties of matching edges across the data set. This identification of common edges is often burdensome and computational intensive. Here, we present an approach that is different from inferring a new network based on common features. Instead, we select one network as a graph prototype, which then represents a set of comparable network objects, as it has the least average distance to all other networks in the same set. We demonstrate the usefulness of the graph prototyping approach on a set of prostate cancer networks and a set of corresponding benign networks. We further show that the distances within the cancer group and the benign group are statistically different depending on the utilized
A Large Scale Analysis of InformationTheoretic Network Complexity Measures Using Chemical Structures
, 2009
"... This paper aims to investigate informationtheoretic network complexity measures which have already been intensely used in mathematical and medicinal chemistry including drug design. Numerous such measures have been developed so far but many of them lack a meaningful interpretation, e.g., we want t ..."
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This paper aims to investigate informationtheoretic network complexity measures which have already been intensely used in mathematical and medicinal chemistry including drug design. Numerous such measures have been developed so far but many of them lack a meaningful interpretation, e.g., we want to examine which kind of structural information they detect. Therefore, our main contribution is to shed light on the relatedness between some selected information measures for graphs by performing a large scale analysis using chemical networks. Starting from several sets containing real and synthetic chemical structures represented by graphs, we study the relatedness between a classical (partitionbased) complexity measure called the topological information content of a graph and some others inferred by a different paradigm leading to partitionindependent measures. Moreover, we evaluate the uniqueness of network complexity measures numerically. Generally, a high uniqueness is an important and desirable property when designing novel topological descriptors having
Philosophy of Mathematical Chemistry: A Personal Perspective
 HYLE International Journal for Philosophy of Chemistry
"... Abstract: This article discusses the nature of mathematical chemistry, discrete mathematical chemistry in particular. Molecules and macromolecules can be represented by model objects using methods of discrete mathematics, e.g., graphs and matrices. Mathematical formalisms are further applied on the ..."
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Abstract: This article discusses the nature of mathematical chemistry, discrete mathematical chemistry in particular. Molecules and macromolecules can be represented by model objects using methods of discrete mathematics, e.g., graphs and matrices. Mathematical formalisms are further applied on the model objects to distill various quantitative characteristics. The end product of such an exercise can be a better understanding of chemistry, the development of quantitative scales for qualitative notions of chemistry, or an illumination of the structural basis of chemical and biological properties. The aforementioned aspects of mathematical chemistry are discussed based on my own practitioner’s perspective.
How Good Can the Characteristic Polynomial Be for Correlations?
, 2007
"... Abstract: The aim of this study was to investigate the characteristic polynomials resulting from the molecular graphs used as molecular descriptors in the characterization of the properties of chemical compounds. A formal calculus method is proposed in order to identify the value of the characterist ..."
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Abstract: The aim of this study was to investigate the characteristic polynomials resulting from the molecular graphs used as molecular descriptors in the characterization of the properties of chemical compounds. A formal calculus method is proposed in order to identify the value of the characteristic polynomial parameters for which the extremum values of the squared correlation coefficient are obtained in univariate regression models. The developed calculation algorithm was applied to a sample of nonane isomers. The obtained results revealed that the proposed method produced an accurate and unique solution for the best relationship between the characteristic polynomial as molecular descriptor and the property of interest.