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

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Let G¹(V,E₁) and G²(V,E₂) be two networks on the same vertex set V and consider the union of edges G(V, E₁ ∪ E₂). This paper studies the stability of the Degree, Betweenness and Eigenvector Centrality of the resultant network, G(V, E₁ ∪ E₂). Specifically assume v¹max and vᶜmax are the highest centrality vertices of G¹(V,E₁) and G(V, E₁ ∪ E₂) respectively, we want to find Pr(v¹max = vᶜmax).