On the Structure and Efficient Computation of IsoRank Node Similarities

The alignment of protein-protein interaction (PPI) networks has many applications, such as the detection of conserved biological network motifs, the prediction of protein interactions, and the reconstruction of phylogenetic trees [1, 2, 3]. IsoRank is one of the first global network alignment algorithms [4, 5, 6], where the goal is to match all (or most) of the nodes of two PPI networks. The IsoRank algorithm first computes a pairwise node similarity metric, and then generates a matching between the two node sets based on this metric. The metric is a convex combination of a structural similarity score (with weight $ \alpha $) and an extraneous amino-acid sequence similarity score for two proteins (with weight $ 1 - \alpha $). In this short paper, we make two contributions. First, we show that when IsoRank similarity depends only on network structure ($\alpha = 1$), the similarity of two nodes is only a function of their degrees. In other words, IsoRank similarity is invariant to any network rewiring that does not affect the node degrees. This result suggests a reason for the poor performance of IsoRank in structure-only ($ \alpha = 1 $) alignment. Second, using ideas from [7, 8], we develop an approximation algorithm that outperforms IsoRank (including recent versions with better scaling, e.g., [9]) by several orders of magnitude in time and memory complexity, despite only a negligible loss in precision.