Evaluation of the Topological Agreement of Network Alignments

Aligning protein interaction networks (PPI) of two or more organisms consists of finding a mapping of the nodes (proteins) of the networks that captures important structural and functional associations (similarity). It is a well studied but difficult problem. It is provably NP-hard in some instances thus computationally very demanding. The problem comes in several versions: global versus local alignment; pairwise versus multiple alignment; one-to-one versus many-to-many alignment. Heuristics to address the various instances of the problem abound and they achieve some degree of success when their performance is measured in terms of node and/or edges conservation. However, as the evolutionary distance between the organisms being considered increases the results tend to degrade. Moreover, poor performance is achieved when the considered networks have remarkably different sizes in the number of nodes and/or edges. Here we address the challenge of analyzing and comparing different approaches to global network alignment, when a one-to-one mapping is sought. We consider and propose various measures to evaluate the agreement between alignments obtained by existing approaches. We show that some such measures indicate an agreement that is often about the same than what would be obtained by chance. That tends to occur even when the mappings exhibit a good performance based on standard measures.