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Topological information indices

The idea of the topological information indices is to apply the general formula for information entropy by Shannon [26,27] to chemical graphs. For that purpose, an equivalence relation is defined partitioning the n vertices of a graph in k disjoint sets with cardinality , with . Then the following indices are defined [4,12,28,29] setting :

 

SIC is stands for structural information content, while CIC means complementary information content. These can be computed for different underlying equivalence relations. In this paper, we only consider the first order neighborhood [12,29]. Here two vertices of the molecular graph (including hydrogens) are considered equivalent iff they have equal atom types, and for each neighbor of the first vertex there exists a neighbor of the second one of the same type and the same connectivity to the atom in question.



wieland@btm2d1.mat.uni-bayreuth.de