The distance-weigthed influence of a node \(X_j\) on an output node \(X_i\) in a Bayesian network is $$DWI(X_j,X_i,w)= \sum_{s\in S_{ji}}w^{|s|},$$ where \(S_{ji}\) is the set of active trails between \(X_j\) and \(X_i\), \(w\in(0,1]\) is an input parameter, and \(|s|\) is the length of the trail \(s\).