a vertex $v_i$ is defined as $d_i=\sum_{i \neq j}^N A_{ij}$, which is the total number of edges that are connected to node $v_i$. The degree matrix $D$ can be defined as $$\begin{aligned}
\label{eq:couple_matrix27}
D_{ij}=\begin{cases} \begin{array}{ll}
            \sum_{i \neq j}^N A_{ij} & i=j\\
            0 & i \neq j.
          \end{array}
\end{cases}\end{aligned}$$ With these two matrices, one can defined Laplacian matrix as $L=D-A$. The Laplacian matrix is also known as admittance matrix, Kirchhoff matrix or discrete Laplacian. It is widely used to represent a graph. More specifically, it can be expressed as, $$\begin{aligned}
\label{eq:couple_matrix26}
L_{ij}=\begin{cases} \begin{array}{ll}
            -1 & i \neq j~{\rm and} ~ (v_i,v_j) \in E\\
                        -\sum_{i \neq j}^N L_{ij} &i=j\\
            0 &{ \rm otherwise.}
          \end{array}
\end{cases}\end{aligned}$$ For example, the adjacency, degree and Kirchhoff matrices for the graph in Fig. \[fig:GRAPH\] are, respectively [$$\begin{aligned}
\label{eq:graph_matrix}
A=\left( \begin{array}{llllllll}
            0  &1  &0 &0  &0  &0  &0  &1  \\
            1  &0  &1 &0  &0  &0  &0  &0  \\
            0  &1  &0 &1  &0  &0  &1  &0  \\
            0  &0  &1 &0  &1  &0  &1  &0  \\
            0  &0  &0 &1  &0  &1  &0  &0  \\
            0  &0  &0 &0  &1  &0  &1  &0  \\
            0  &0  &1 &1  &0  &1  &0  &1  \\
            1  &0  &0 &0  