Let \(V_{n}\) be a set of \(n\) elements (\emph{e.g.} graph with \(n\) vertices). For some finite \(m > 0\) and each \(k \in \{ 1,\ldots, m \}\) let \(S_{k} \subseteq V_{n}\) and \(\lambda_{k} > 0\). For \(1 \leq i < j \leq n\), define \[ {δ(S_k)}_i,j = \begin{cases} 1 & \text{ if } |S_{k} \cap \{ i,j \}| = 1 \\ 0 & \text{ otherwise}. \end{cases} \] Then \(d_{w}(i,j) = \sum_{k} \lambda_{k}\delta(S_{k})_{i,j}\) defines a semimetric on \(V_{n}\). Note that if we have a graph with \(n\) vertices, this semimetric is based on a partition of the vertices, it does not take the edges of a graph into account (hence \(S_{k}\) and \(V_{n}\setminus S_{k}\) may not be connected components).