Simple graph representation

Many of the descriptors which can be calculated from the 2D structure rely upon the molecular graph representation because of the need for rapid calculations. Kier and Hall have developed a large number of topological indices, each of which characterises the molecular structure as a single number [Hall and Kier 1991]. Every non-hydrogen atom ir the molecule is characterised by two delta values, the simple delta Si and the valence delta SJ ... 

Pairwise relationships such as (2.3a-d) can be represented by simple 2-dimensional (2D) graphs, but the full PVT behavior of the equation of state requires a 3-dimensional (3D) representation (for fixed n = 1). Figure 2.1 illustrates some simple graphical representations of the ideal gas equation of state (2.2). Figure 2.1a illustrates Boyle s law (2.3a) in... 

A simple measure of structural complexity of a molecule based on its graph representation G compared with the parent -> complete graph K(Q, i.e. the complete graph with the same number of vertices. It is defined as ... 

Many operations on Boolean functions can be implemented by simple graph algorithms that work recursively on their BDD representation in a conventional depth-first fashion. For example if f and g are Boolean functions represented by BDDs, if x, is one of their variables and if op is a generic binary operator, we express f op g as ... 

Chemical structures are typically represented in computer programs as simple graphs, where the atoms are represented by a hst of nodes and the bonds by a list of non-directional edges. We will describe an extension to such a representation which allows properties to be identified with a defined subgraph in a structure these properties are fully searchable at a substructure level. A description of the representation will be given and examples of searching capabilities will be illustrated. An implementation of these techniques has been apphed to homo> polymers, copolymers, non-stoichiometric mixtures, formulations, and superatoms . Other potential uses will also be discussed. These extensions to chemical representation allow us to represent and search a much broader class of chemical substances than the set of discrete chemical structures which have previously been handled. 

A graph paper based on this type of relationship can be obtained. It permits convenient graphical representation of size distribution data (as shown in Fig 3) even if the distribution does not follow a log-probability relationship. In addition, the assumption of a log-probability distribution as an approximation permits simple conversion from one basis of representing size distribution, mean size, or median size to another basis... 

Van Zijll Langhout developed graphs for compounds consisting of C, H and S, analogous to the graphical representation of C -H -O compounds of Van Krevelen46. These graphs, of which Fig. 63 is an example, are based on the ultimate analysis, and can be applied to identify pure sulphur compounds and to analyse simple mixtures... 

The advantage of the following methods of graphical representation is the clear and simple presentation of the essential facts. Simple charts, like bar charts, x-y scatter diagrams or pie diagrams, which are also available in 3D-form are also suited to visual representation of data. They are not described because this section is devoted to treatment of multivariate data. Graphs for control charts, particulary for quality assurance and control, can be found in [FUNK et al., 1992 AQS, 1991]. 

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