Network alignment (NA) compares networks with the goal of finding a node mapping that uncovers highly similar (conserved) network regions. Existing NA methods are homogeneous, i.e., they can deal only with networks containing nodes and edges of one type. Due to increasing amounts of heterogeneous network data with nodes or edges of different types, we extend three recent state-of-the-art homogeneous NA methods, WAVE, MAGNA++, and SANA, to allow for heterogeneous NA for the first time. We introduce several algorithmic novelties. Namely, these existing methods compute homogeneous graphlet-based node similarities and then find high-scoring alignments with respect to these similarities, while simultaneously maximizing the amount of conserved edges. Instead, we extend homogeneous graphlets to their heterogeneous counterparts, which we then use to develop a new measure of heterogeneous node similarity. Also, we extend S3, a state-of-the-art measure of edge conservation for homogeneous NA, to its heterogeneous counterpart. Then, we find high-scoring alignments with respect to our heterogeneous node similarity and edge conservation measures. In evaluations on synthetic and real-world biological networks, our proposed heterogeneous NA methods lead to higher-quality alignments and better robustness to noise in the data than their homogeneous counterparts. The software and data from this work is available at https://nd.edu/~cone/colored_graphlets/.

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Motivation Prediction of node and graph labels are prominent network science tasks. Data analyzed in these tasks are sometimes related: entities represented by nodes in a higher-level (higher-scale) network can themselves be modeled as networks at a lower level. We argue that systems involving such entities should be integrated with a “network of networks” (NoN) representation. Then, we ask whether entity label prediction using multi-level NoN data via our proposed approaches is more accurate than using each of single-level node and graph data alone, i.e., than traditional node label prediction on the higher-level network and graph label prediction on the lower-level networks. To obtain data, we develop the first synthetic NoN generator and construct a real biological NoN. We evaluate accuracy of considered approaches when predicting artificial labels from the synthetic NoNs and proteins’ functions from the biological NoN. Results For the synthetic NoNs, our NoN approaches outperform or are as good as node- and network-level ones depending on the NoN properties. For the biological NoN, our NoN approaches outperform the single-level approaches for just under half of the protein functions, and for 30% of the functions, only our NoN approaches make meaningful predictions, while node- and network-level ones achieve random accuracy. So, NoN-based data integration is important. Availability The software and data are available at https://nd.edu/~cone/NoNs. Supplementary information Attached to the submission.

In this study, we deal with the problem of biological network alignment (NA), which aims to find a node mapping between species' molecular networks that uncovers similar network regions, thus allowing for the transfer of functional knowledge between the aligned nodes. We provide evidence that current NA methods, which assume that topologically similar nodes (i.e., nodes whose network neighborhoods are isomorphic-like) have high functional relatedness, do not actually end up aligning functionally related nodes. That is, we show that the current topological similarity assumption does not hold well. Consequently, we argue that a paradigm shift is needed with how the NA problem is approached. So, we redefine NA as a data-driven framework, called TARA (data-driven NA), which attempts to learn the relationship between topological relatedness and functional relatedness without assuming that topological relatedness corresponds to topological similarity. TARA makes no assumptions about what nodes should be aligned, distinguishing it from existing NA methods. Specifically, TARA trains a classifier to predict whether two nodes from different networks are functionally related based on their network topological patterns (features). We find that TARA is able to make accurate predictions. TARA then takes each pair of nodes that are predicted as related to be part of an alignment. Like traditional NA methods, TARA uses this alignment for the across-species transfer of functional knowledge. TARA as currently implemented uses topological but not protein sequence information for functional knowledge transfer. In this context, we find that TARA outperforms existing state-of-the-art NA methods that also use topological information, WAVE and SANA, and even outperforms or complements a state-of-the-art NA method that uses both topological and sequence information, PrimAlign. Hence, adding sequence information to TARA, which is our future work, is likely to further improve its performance. The software and data are available at

Background Network alignment (NA) can transfer functional knowledge between species’ conserved biological network regions. Traditional NA assumes that it is topological similarity (isomorphic-like matching) between network regions that corresponds to the regions’ functional relatedness. However, we recently found that functionally unrelated proteins are as topologically similar as functionally related proteins. So, we redefined NA as a data-driven method called TARA, which learns from network and protein functional data what kind of topological relatedness (rather than similarity) between proteins corresponds to their functional relatedness. TARA used topological information (within each network) but not sequence information (between proteins across networks). Yet, TARA yielded higher protein functional prediction accuracy than existing NA methods, even those that used both topological and sequence information. Results Here, we propose TARA++ that is also data-driven, like TARA and unlike other existing methods, but that uses across-network sequence information on top of within-network topological information, unlike TARA. To deal with the within-and-across-network analysis, we adapt social network embedding to the problem of biological NA. TARA++ outperforms protein functional prediction accuracy of existing methods. Conclusions As such, combining research knowledge from different domains is promising. Overall, improvements in protein functional prediction have biomedical implications, for example allowing researchers to better understand how cancer progresses or how humans age.