Weighted graph

A weighted graph assigns a symmetric nonnegative conductance ${\mu }_{xy}$ to each edge. With killing weights ${\kappa }_x$, the associated discrete-time walk moves from $x$ to $y$ with probability ${\mu }_{xy}/{\mu }_x$ and is killed with probability ${\kappa }_x/{\mu }_x$, where ${\mu }_x={\kappa }_x+{\sum }_y{\mu }_{xy}$.

The killing measure assigns the weight ${\kappa }_x$ of the transition from $x$ to a cemetery state.