Reduced graph node

Figure 1.12. Examples of reduced graphs. Nodes corresponding to aromatic rings (Ar), aliphatic rings (R), functional groups (F) and linking groups (L) are shown (adapted from Gillet el al. 2003)...

Table S.l Types of reduced graph nodes in precedence order top to bottom left to right.

The first two stages were described in the section on screening techniques. Comparison of EPVs within reduced graph nodes provides a more detailed level of description and is also used to identify structure matches and non-matches as early as possible in the succession of search operations. For example, there are cases where a structure match can already be identified during the node search. The conditions required for the coincidence of a node match with a structure match for a given query node/file node pair are ... 

The Morgan algorithm 5> is a device used by the Chemical Abstracts Service for assigning indices to the nodes of constitutional formulas whose H-atoms have been omitted, i. e. their reduced graphs. If the indices of all atoms are needed, e.g. for the representation of stereochemistry, an additional procedure is needed for establishing those for the H-atoms. Constitutional symmetry is not indicated directly by Morgan indices. 

For database searching, pharmacophores are best defined by all possible distances between chosen groups or features (pharmacophore points). Therefore, as illustrated in Figure 1.13, they are best represented as a molecular graph (similar to reduced graphs). In this case, different from conventional graphs, however, nodes correspond to points (or centroids) and edges to inter-point distances, rather than bonds. 

In the ring/non-ring reduced graph, therefore, the components of the structure are reduced to nodes of which there are two basic t5q>es, the ring node and the non-ring node. This is readily illustrated for a specific structure in Figure 2. 

These methods result in substantial reductions in the numbers of nodes handled in the reduced representation. In the ring/non-ring reduced graphs, this averages about a... 

The function edge is used to construct graphs of type t. It reduces the node consisting of variable x and the successors high returns a labelled edge F ... 

Let us apply the operation merging of nodes to each subset N, of nodes of our graph G. Let G be the reduced graph obtained in this manner. Thus with... 

Let us arrange the subgraphs G° in the manner that G , , G - K < K) are those subgraphs which are not isolated nodes observe that if G is an isolated node, the corresponding (scalar) equation (node balance) in (3.2.2) becomes automatically one of the node balances of the reduced graph G. Having selected a reference node in each G for k = I, , K , let B be the reduced incidence matrix of G, thus B is of full row rank let further A, be the corresponding... 

Having completed the classification according to steps (a) and (b) above, we can make use of the additional information obtained in the described manner. First, the reduced graph G determines, having selected a reference node, the reduced incidence matrix A. It is the matrix occurring in (3.2.4)2, thus in the constraint equation for the measured vector m (in fact, only for the subvector m of redundant variables). The equation is employed for adjusting the given values if the components of m"" have been actually measured then for reconciliation by statistical methods. 

Recall that a connected component can also consist of one (isolated) node, with empty subset of incident arcs. Having merged the nodes of each N,j in G we have the reduced graph G see Fig. 3-7. The K nodes of G correspond uniquely to the K subsets N, of N. By the graph reduction (merging), we have deleted all the arcs j e J°, and some arcs j g J in addition (subset J c J ). The arc set of G , denoted by J, consists of the remaining (not deleted) arcs j e J. Thus J"" is partitioned... 

In a system of mass balance equations, the equation (9.6.7)j can be formulated as the mass balance of the reduced graph G, hence the residual r (9.6.8a) represents a vector of node imbalances. Then also an analysis of residuals makes sense see Remark to Section 9.4. 

Observe finally that if the original G was connected then a fortiori the reduced graph G is connected. [Indeed, a path between any two nodes and of G can be obtained by merging on a path between some e N, and... 

One can obtain the reduced graph as above by merging the nodes connected by streams that are not fixed. It reads... 

Finally the integration of these two screening methods is described, i.e., the inclusion of fragment and ring screens within the nodes of a reduced graph. 

The differentiation of the reduced graph is increased by the inclusion of structural information within the nodes. This is achieved by combining information... 

Structural information is accumulated for the nodes of a reduced graph by conflating the parameter values derived by the collapse of two or more partial structures which constitute that node. For instance, the non-ring node which is generated by the collapse of the two alternative substituents Cl-7 alkoxy (C(l-7)E(0)T<0-)Z<1)) and -CH = C(CH3)-CH = CH2 (C(5)E<2)T<1)Z<0 is specified by an accumulated node parameter list with parameter values of C<1-7)E<0,2)T(0-) Z(O-l). These are derived from the parameter values of the respective generic and specific parameter list, by the bubble-up process. 

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