We choose the following: we first represent each node (pivot language word) in a graph as the vector of distances to all other nodes.
to u ∈ is then defined as the average distance (Euclidean norm) of the so represented nodes in the graphs: Finally, we define the (syntacto-)semantic distance D( , ) of two languages and as the average graph distance over all N − 1 pivots (l and l excluded): By summing over pivots, we effectively 'integrate out' the influence of the pivot language, leading to a 'pivot independent' language distance calculation.