  Networks are abundant in the life sciences. Outstanding challenges include
how to characterize similarities between networks, and in extension how to
integrate information across networks. Yet, network alignment remains a core
algorithmic problem. Here, we present a novel learning algorithm called
evolutionary heat diffusion-based network alignment (EDNA) to address this
challenge. EDNA uses the diffusion signal as a proxy for computing node
similarities between networks. Comparing EDNA with state-of-the-art algorithms
on a popular protein-protein interaction network dataset, using four different
evaluation metrics, we achieve (i) the most accurate alignments, (ii) increased
robustness against noise, and (iii) superior scaling capacity. The EDNA
algorithm is versatile in that other available network alignments/embeddings
can be used as an initial baseline alignment, and then EDNA works as a wrapper
around them by running the evolutionary diffusion on top of them. In
conclusion, EDNA outperforms state-of-the-art methods for network alignment,
thus setting the stage for large-scale comparison and integration of networks.
