A　method　is　proposed　to　construct　the　weighted　amino　acid　network.　The　weight　of　the　link　is　based　on　the　contact　energy　between　residues.　For　the　197　proteins　with　low　homology,　the　＂small-world＂　property　was　studied　based　on　this　method.　Additionally,　analyses　were　carried　out　for　the　statistic　characteristics　of　the　network　parameters,　the　influence　of　the　weight　on　the　network　parameters,　the　network　parameter　difference　of　amino　acids,　and　the　links　between　the　hydrophobic　and　hydrophilic　residues.　Using　this　method,　we　studied　the　network　parameter　change　for　the　protein　chymotrypsin　inhibitor　2　(CI2)　on　its　high-temperature　unfolding　pathway.　It　is　found　that　the　unfolding　of　the　protein　is　mainly　exhibited　as　the　derogation　of　the　hydrophobic　core　and　the　shortest　path　length　rise　in　the　unfolding　process.　This　work　is　helpful　for　studies　of　protein　folding　and　the　relationship　between　structure　and　function　using　complex　network　theory.