From: Joerg W. <we...@in...> - 2005-02-06 14:49:16
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Hi all, minor bug fix release (atom label caching indexing for last atom in a molecule, for some properties only) and minor feature enhancement (characteristic polynomial). After looking for a reasonable interpretation for eigenvalues of the adjaceny matrix i have found the analogy to the hueckel matrix.This is fantastic, but not really general for all weighted adjaceny matrices, with user defined atom and bond labels. Nontheless there exists still a much better analytical interpretation of the (weighted) adjaceny matrix (with atom and bond labels) which is called the characteristic polynomial. If the polynomials (their coefficients) of two graphs are identical then those graphs are isospectral (spectral theory of graphs). Using the Heilbronner theorem, we can check and interpret substructural fragments, at least on a linear fragment level. Heilbronner theorem: P(G)=P(G-eij)-P(G-vi-vj)-2*sum(P(G-Z)) P(G) is the characteristic polynomial in its general form any edge eij G-eij: Graph without this edge G-vi-vj: Graph without edge atoms sum(P(G-Z)): Sum over ALL rings Z, which contains eij. Please note that this means really all rings and not only the SSSR ring set, so this is quite nice, but hard to be calculated. The characteristic polynomial is calculated by using the Le Verrier-Faddeev-Frame method, which uses a framework of recursive matrix operations. Kind regards, Joerg Kurt Wegner Dipl. Chem. Joerg K. Wegner Center of Bioinformatics Tuebingen (ZBIT) Department of Computer Architecture Univ. Tuebingen, Sand 1, D-72076 Tuebingen, Germany Phone: (+49/0) 7071 29 78970 Fax: (+49/0) 7071 29 5091 E-Mail: mailto:we...@in... WWW: http://www-ra.informatik.uni-tuebingen.de -- Never mistake motion for action. (E. Hemingway) Never mistake action for meaningful action. (Hugo Kubinyi,2004) |