Identifying protein clusters is an important Task carried out in the field of bioinformatics. There are several methods to store protein structures. We use Graph Spectra to do this operation by using normalized Laplacian matrix to represent graph [7, 9]. Then set of eigenvalues of normalized Laplacian matrix are calculated to create graph spectra after sorting the eigenvalues in descendant order. Using graph spectra allows to speed up the SOM network training in comparison with the direct calculation on graphs [3, 10]. The normalized Laplacian matrix is defined as follows: […]
Graph distance based on graph spectra between two graphs is Euclidean distance between graph spectra of two graphs. Let s and t be graph spectra of two graphs. Graph distance based on graph spectra of graph s and t is calculated as follows: […]
Using graph distance based on graph spectra to measure the distance between two graphs is an effect way for faster comparison with the complexity of graphs having more than 400 vertices. It reduces the comparison time between graphs when performing. To calculate the distance between two graphs with different number of vertices, we use function Pad (v, x, k). This function will fill k values of x to the end of the vector v [2]. In the above example, the graph spectra of graph G1 and graph G2 are as follows: […]
Since graph G1 has number of vertices less than graph G2, we need to insert two zeros at the end of the graph spectra of graph G1. Graph spectra of graph G1 after filling value 0 is: […]
The distance between graph G1 and graph G2 is Euclidean distance between graph spectra λ(G1) and graph spectra λ(G2). In this case, the distance between graph G1 and G2 is 2.89.