A novel link index X proposed deals with the feature of molecule graph, the property of vertical atom and the bonding of atoms connected to each other. Matrices are used to represent these characters. Relationship between link indices X and the boiling point of alkanes is investigated based on molecular topology. It is found that X is highly correlated with the boiling point of alkanes. Based on the X and boiling point regression equations, the boiling point of other alkanes molecules, and the error analysis are discussed. The results show that the model developed can make a better agreement between predicted and observed values for the biodegradability of the tested compounds than ever before.