Quantitative Structure-Activity Relationships based on molecular descriptors calculated with Correlation Weights of Local Graph Invariants were developed to model the toxicity of aliphatic compounds to the 50% population growth inhibition. The relationships were computed on the basis of Labeled Hydrogen-Filled Graphs and correlation weights were obtained by an optimization to render as large as possible correlation coefficients between log(IGC(50)(-1)) and descriptors calculated with correlation weights. Morgan extended connectivity indices of zero, first, and second orders, paths of lengths two and three and valence shells of second and third ranges have been tested as local invariants of the Labeled Hydrogen-Filled Graphs. The best quantitative relationship obtained from the optimization of correlation weights is that one based on the valence shell of range two. First, second, and third order fitting equations were determined and statistical results are better than other similar data for the same molecular set.