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

Let G(V,E1) and G (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 v max and v max are the highest centrality vertices of G(V,E1) and G(V,E1 ∪ E2) respectively, we want to find Pr(v max = v max). ar X iv :1 30 9. 66 29 v1 [ nl in .A O ] 2 5 Se p 20 13 Stability of the Centrality of Unions of Networks on the Same Vertex Set 2