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

Abstract

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 $v_{max}^1$ and $v_{max}^c$ are the highest centrality vertices of $G^1(V,E_1)$ and $G(V,E_1\cup E_2)$ respectively, we want to find $Pr(v_{max}^1=v_{max}^c)$.

12 pages with 6 figures