The edge-weigthed influence of a node \(X_j\) on an output node \(X_i\) in a Bayesian network is $$EWI(X_j,X_i)= \sum_{s\in S_{ji}}\left(\prod_{(k,l)\in s}\delta_{kl}\right)^{|s|},$$ where \(S_{ji}\) is the set of active trails between \(X_j\) and \(X_i\), \(\delta_{kl}\) is the strength of an edge between \(X_k\) and \(X_l\), and \(|s|\) is the length of the trail \(s\).