= Boundary-reaching stencil connectivity
A finite elliptic stencil has boundary-reaching connectivity when every unknown node has a directed path of strictly positive neighbor coefficients to a prescribed boundary node. For $L\psi_p=\sum_{r\ne p}c_{p,r}\psi_r-c_{p,p}\psi_p$, with $c_{p,r}\geq0$ and $c_{p,p}\geq\sum_{r\ne p}c_{p,r}$, a nonnegative interior maximum of a subsolution $L\psi\geq0$ propagates along every positive-weight edge. The path condition carries it to the boundary, proving the <discrete maximum principle>. Connectedness of the underlying geometric domain alone does not imply this graph property.
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