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Overview John M. IV: The Data. Booth, et al. Gregory Paris. VI: Searching Chemical Structures.

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IX: Methods for Data Analysis. X: Applications. Property Relationships Peter C. Spectra Correlations.

## Handbook of Chemoinformatics Algorithms: 1st Edition (Hardback) - Routledge

Farnum, et al. Shipping Add to Cart. Further versions. Description Content Reviews Author information This handbook provides the first-ever inside view of today's integrated approach to rational drug design. Tudor I. He was born in Timisoara Romania where he did all his studies including his Ph. He is interested in chemoinformatics, virtual screening, QSAR, and lead and drug discovery.

XU, J.

ROZAS, 1. Downs 5. The most extensive review of ring perception algorithms for chemical graphs to date was published in by the present author [ 11, with a discussion of twenty-four algorithms and references to many more related algorithms. In addition, discussions related to the theoretical basis for various ring sets were published in [2] and [3]. A further seven algorithms [ for chemical graphs published since were included in a previous version of this article published in [ l l ]. This update includes a further four algorithms [ One consequence is that different terminology is used for the same concepts.

This section outlines the minimum amount of terminology necessary for the rest of the article, and is an amalgam of terms used in graph theory and combinatorics see Chapter 11, Sections 4 and 5. A chemical structure, typically given by a structure diagram, is represented as an undirected graph in which the atoms are the vertices and the bonds are the edges.

Vertices and edges can be colored, i. The valence or degree of each atom is the vertex connectivity; the number of ring bonds attached to an atom is its ring-connectivity. Starting from any vertex of the graph, a tree can be grown to yield a spanning tree, which contains each vertex of the graph once only, and each edge except the chords. The chords are the minimum number of edges required to turn the tree from acyclic to cyclic.

If the graph is disconnected then a spanning tree can be grown for each component of the graph; a ring component contains edges that are all cyclic. Fan et al. A walk is an alternating sequence of connected vertices and edges; if the start and end vertex are the same, and all other vertices and edges occur once only then the walk is a cycle. If a cycle is found from each chord then a fundamental basis set of cycles has been found.

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If in a cycle there are no pairs of vertices joined by an edge that is not in the cycle then it is a simple cycle; all other cycles are complex cycles. If the sum of the sizes of the cycles in a fundamental basis is a minimum then the set is referred to as a minimal cycle basis. Most chemical graphs can be drawn in two dimensions such that no edges cross, in which case the graph is said to be embeddable on a plane. Planar embedment defines regions which have no edges or vertices crossing them and non-regions.

The region defined by the outer boundary of a graph is the infinite region; all other regions are finite regions.

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Finite and infinite regions are always interchangeable by redrawing the graph. A region that is a simple cycle is a simple face. A non-region that is a simple cycle is a cut face. If one simple face is larger than all the other simple faces then it is the maximal simple face; if a simple face is the smallest simple face associated with each of its edges then it is a minimal simple face; all 5.

If a cut face is the smallest simple cycle associated with at least one of its edges then it is a primary cut face; otherwise, if at least one of its edges is associated with a simple cycle of the same size and none smaller then it is a secondary cut face; otherwise it is a tertiary cut face.

The relationships between the various cycles are summarized in Figure 5. The terms can be understood more readily by reference to example graphs. In cubane, Figure 5. The eight 6-edged simple cycles are all tertiary cut faces. In Figure 5. This section summarizes the two basic perception methods, those using graph theory and those using linear algebra, and then discusses some of the pre-processing methods used to make the perception methods more efficient.

Details of all the methods mentioned can be found in the introductions to the papers cited in this article and the papers cited in the review [ The two main methods for finding cycles in the graph are depth-first search and breadth-first search. Depth-first search has lower storage requirements and is generally better for finding all cycles. Breadth-first search is generally faster at finding the smallest cycles. The searching can be used I I to find the cycles directly, or to find all paths between two vertices with subsequent 5.

The searching can also be performed on an incidence or adjacency matrix derived from the graph. Since the paths are stored during search, the correct vertex-edge sequence of a cycle is known once the cycle has been found. If a fundamental basis set of rings can be found then linear algebraic methods can generate every other cycle present in the graph.

Fundamental bases are not generally unique but they always contain ,u cycles. The usual way to find a fundamental basis is to generate a spanning tree. Other cycles can then be generated by either using a depth or breadthfirst search from the ends of the chords of the spanning tree, or by taking the exclusive or XOR of the edges of each combination from 1 to p of the basis cycles. XOR operations are generally very fast, but since binary sets are used for the combinations, the correct vertex-edge sequence of each cycle needs to be looked up afterwards.

A feature common to many of the perception methods using linear algebra is the use of linear independence to determine either a particular fundamental basis or an extension of it [8, Alternatively, a spanning tree can be grown to trace and label all cyclic edges and vertices; subsequent perception can then ignore unlabeled vertices and edges.

Individually processing each ring component of a graph is particularly effective for matrix manipulation methods. Row reordering can identify separate ring components, and the ring components processed by including only the relevant rows.

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Depth and breadth-first searches can use cyclic labeling to avoid crossing from one ring component to another. The simplest 5. If this is done before ring perception proceeds the graph has fewer edges and vertices to search; Balaban et al. A more complex form of graph reduction is shown by the cut-vertex graphs of Downs et al. Different applications have different requirements, and so a variety of ring sets the particular sets chosen from within the wide range available have been defined.

The main factor is usually that the ring set should be unique for a given structure and invariant, i. Given the large number of rings that could be included in a set, a general aim is to include the minimum number of rings necessary to describe the ring system and also to include sufficient rings to describe the ring system adequately for a given application.

The problem is deciding what is necessary and sufficient.

For instance, in cubane, Figure 5. If only the 4-edged simple faces should be included in the ring set for cubane, then how many should be included? Similarly, is norbornane, Figure 5. This section covers nine of the main ring sets used in applications processing chemical structure graphs. The most commonly used ring set is the minimal cycle basis, usually referred to as the smallest set of smallest rings SSSR.

In addition to the ring sets mentioned here, most other published ring sets are heuristic supplements to an SSSR; further details of these can be found in the review [I]. A summary of the contents of each of the ring sets in this section is given in I 5. Each of these ring sets is discussed more fully below, along with brief summaries of the algorithms to find them the original papers should be consulted for full details. If more than one published algorithm for a particular ring set is available then details are given of the one the present author feels is best in terms of efficiency and clarity of the algorithm.

For complex ring systems processing to find the number of cycles can grow exponentially with the number of vertices. Algorithms exist [ 11 that use each of the methods outlined in Section 5.

The most recent algorithm is by Hanser et al.