The aim of these work is to investigate the connection between the eigenvalues and eigenfunctions of a network $\Gamma=(V,E,c)$ and those of its generalized subdivision network $\Gamma'=(V\cup V',E',c')$. This is the network obtained from $\Gamma$ by adding a new vertex in some of its edges. Our interest lies in interpreting the matrix associated with a Schr\"odinger operator of $\Gamma$ as the Schur complementation of a suitable Schr\"odinger operator on $\Gamma$ with respect to a set of ve...
The aim of these work is to investigate the connection between the eigenvalues and eigenfunctions of a network $\Gamma=(V,E,c)$ and those of its generalized subdivision network $\Gamma'=(V\cup V',E',c')$. This is the network obtained from $\Gamma$ by adding a new vertex in some of its edges. Our interest lies in interpreting the matrix associated with a Schr\"odinger operator of $\Gamma$ as the Schur complementation of a suitable Schr\"odinger operator on $\Gamma$ with respect to a set of vertices. This process is known in circuit theory and reletad areas as Kron reduction. The spectrum of some networks obtained as extension from $Gamma$ will be analized.