In order to characterize structures of organic compounds efficiently, equilibrium electronegativities were calculated based on the principle of the balanced electronegativities. The novel topological index AI was proposed by the extending adjacent matrix employing the degree of branching and equilibrium electronegativities which were utilized to dye hydrogen-suppressed graph. Possessing clear physical meaning,AI can distringuish compounds containing multiple bonds and/or heteroatoms. In addition,the path number P2 and P3 were involved as well. ...