Abstract: A method is proposed to construct the weighted amino acid network.The weight of link is based on the mean-square fluctuations of the distance of the contact residue pairs.For the 180 proteins with low homology,the small-world property is studied based on this method.The results show that the average clustering coefficients of the weighted networks are less than that of the unweighted networks.The power-law behavior of clustering coefficients of the weighted and the unweighted networks indicates that they have significant hierarchical structure,which mainly originates from the hierarchical behavior of the hydrophobic amino acid network.Finally,the comparison of the values calculated from the weighted network with that of the unweighted network shows that the weighted network has an obviously higher power to recognize the folding cores.These results reveal that the weighted amino acid network contains more information about amino acids than that of the unweighted network.