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Spectral density approach for distinguishing graphs was studied in this paper. Firstly, spectral density approach was testified for being effective in distinguishing different graphs by making comparisons among the spectrums of three different kind of graphs, the ER random graph, BA scale-free graph and the Internet topology graph. Secondly, we focused our studies on the properties of Internet graph that its spectrum could represent, and found that in standard spectral density analysis part, we found that the spectral density plot of Internet graph has a feature of having a maximum when Â¿=0 and the second maximum when Â¿=0.5 around. In SLS analysis part, we found the SLS spectrum had a set of highest tuples when SLS=1 and second highest tuples when SLS>2. Besides, a relationship of the power law distribution was observed when SLS>2, but there is no power-law relationship found when SLS. What was found here could be used to identify an Internet topology graph properties.