Disadvantages of the L-RWGK include (i) its compute-and memory-intensity to evaluate, hence poor scalability to large molecules and large data sets and (ii) tottering. Expanding on (ii): by definition, the vertices in a walk (see eqn. 1) may not be distinct (then, it would be a path). Thus, long walks that totter back and forth between the same few vertices-e.g., at the extreme: w = (u, v , u, v , ..., u, v )-are accounted for in the L-RWGK. These walks do not contribute extra information about the similarity of two graphs-e.g., for our extreme example, no more information beyond the length-2 walk (u, v ). Tottering thus could lead to a "dilution" of the similarity metric expressed by the random walk kernel. Modification of the random walk kernel can prevent tottering walks from contributing to the similarity metric.