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.