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

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 $Pr(v^1_{ max} = v^c_{ max})$.

Categories: nlin.AO cs.SI math.CO