Turning SDP into vectorized form I have a graph with edge-set E and the following SDP (page 8 here)

I'm trying to use CVXOPT to solve this problem, which asks for SDP to be expressed in vectorized form as below:

How do I go about turning my SDP into this form?
Update
From suggestion of Joachim Dahl it's easier to figure out values from the dual form. We need to set $G_1,h_1$ and $c$ as follows
$$G_1=\left(\begin{array}{c}
\text{vec}(I)\\\\
\text{vec}(U_{e1})\\\\
\text{vec}(U_{e2})\\\\
\cdots\\\\
\text{vec}(U_{em})
\end{array}\right)$$
here $I$ is $n\times n$ identity matrix, $\text{vec}(A)$ is matrix $A$ taken as vector in row-major vector form, $U_{ek}$ is a $0,1$-valued matrix where entry $i,j$ is 1 iff $i,j$ is in the edge $ek$.
$$c = (-1,0,0,0,0,\ldots,0)$$
$$h_1=- \left(\begin{array}{ccc}
1&1&\ldots\\\\
1&1&\ldots\\\\
\ldots&\ldots&\ldots
\end{array}
\right)$$
Note that for a graph with $n$ nodes and $m$ edges, $G_1$ is an $m+1\times n^2$ matrix, $c$ is a vector of length $m+1$ and $h_1$ is an $n\times n$ matrix. Matrix $X$ from original formulation is the $z_1$ parameter, an $n^2$ vector representing the matrix in row-major form

You can put $h_1 = 0$ and put $$ G_1 = -\frac{1}{2} \sum_{i \leq j} (e_{ij}+e_{ji}) x_{ij}. $$ This way you have that $x_{ij}$ are the entries of a PSD. You can add your constraints using $Ax=b$. Finally, notice that your objective function is linear in the entries of the matrix.
