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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 thestability of the Degree, Betweenness and Eigenvector Centrality of theresultant 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 $Pr(v^1_{max} = v^c_{max})$.

Stability of the Centrality of Unions of Networks on the Same Vertex Set