  Let $G^1(V,E_1)$ and $G^2(V,E_2)$ be two networks on the same vertex set $V$
and consider the union of edges $G(V, E_1 \cup E_2)$. This paper studies the
stability of the Degree, Betweenness and Eigenvector Centrality of the
resultant network, $G(V, E_1 \cup E_2)$. Specifically assume $v^1_{max}$ and
$v^c_{max}$ are the highest centrality vertices of $G^1(V,E_1)$ and $G(V, E_1
\cup E_2)$ respectively, we want to find $Pr(v^1_{max} = v^c_{max})$.
