A consistent distance matrix $D$ on a collection of taxa $s_1, s_2, \ldots, s_n$ is consistent if there exists a tree $T$ that models the evolutionary relationships encoded by the distances in $D$.

More precisely, for $D$ to achieve consistency, we demand that $T$ is a weighted, unrooted binary tree, and that the distance between $s_j$ and $s_k$ in $T$ is equal to $D_{j,k}$.