Spectral methods in which they are based on matrix eigenvectors are widely used in network data analysis, especially for community detection. These classical approaches are based on graph associated matrix (adjacency matrix) and related matrices, nevertheless go wrong with sparse networks, which they have a lot of interest in practice. The spectrum of the non-backtracking matrix, an alternate matrix representation of a network that shows a behavior in the sparse limit, has recently been presented as a solution to this problem. However, the use of this matrix was limited for a specified number of communities. We are presenting a matrix for the graph and showing that it can be using for different number of communities.