Is Bray curtis measure consider similarity measure

the distance (i.e. dissimilarity) between any pair of nodes i and j is bounded in this space: D(i, IDX(i)) − D(j, IDX(j)) ≤ dist(i,j) ≤ D(i, IDX(i)) + D(j, IDX(j)). is this equation D(i, IDX(i)) − D(j, IDX(j)) / D(i, IDX(i)) + D(j, IDX(j)) consider a similarity ? why? where previous equation satisfy triangle inequality