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In this paper, we would like to present our research result to build a graph clustering system using the SOM neural network and graph spectra. We use this system to support the visualization of similar protein structures in graph database of protein structures. Graph spectra is a set of eigenvalues of the normalized Laplacian matrix representing the graph. These eigenvalues are sorted in descendant order. We create a feature vector of sorted eigenvalues in descendant order to represent graph. SOM neural network is used to cluster the graph spectra; graph distance is Euclidean distance between graph spectra. Using graph spectra, we can improve the speed of training phase of SOM neural network. After clustering, the 2D SOM output layer will create the clusters of similar protein structures. By putting 2D SOM output layer on the computer display, we can visualize the similar protein structures of database by moving around the computer display. Our proposed solution was tested with the protein structures downloaded from SCOP database which was created by manual inspection and automated methods for description of the structural and evolutionary relationships between all proteins known. Our results are compared with the SCOP.