Given graph $G(V,E)$. Every vertice $v$ has its weight $w(v)$. 
I want to work with $$\sum_{(u,v)\in E}w(u)w(v)$$
I think it should many good approaches to this object?
Furhermore, is there method of calculating this sum via incidence matrix?

Incidence matrix is $|V|\times|V|$ $(0,1)$-matrix with entries $a(u,v)$, such that
$$
a(u,v)=
    \begin{cases} 
      1 & (u,v)\in E \\
      0 & otherwise 
   \end{cases}
$$