Mathematical description and inference of complementarity mechanisms in complex networks.

In this project, I aim to study the role of complementarity mechanisms in networked systems. Examples of complementarity-driven networks include interdisciplinary collaboration networks, networks of interacting proteins, and food webs. In all aforementioned systems, connections are established between nodes with complementary properties. The grand challenge of the present project is the lack of mathematical intuition behind the complementarity. While we casually use this term daily, we lack rigorous definitions of complementarity in mathematical sciences. Complementarity is often confused with similarity. The latter is one of the key principles underlying the formation of social networks: the more similar individuals are the higher is the chance for social interaction between them. Latent geometry provides an elegant way to model similarity in social networks. Network nodes are viewed as points in an underlying latent or hidden space, such that distances between them quantify node similarities: the smaller the distance between the two nodes the more similar they are. It is the similarity interpretation of latent distances that lies at the origin of many applications of network embeddings, including link prediction, node classification, network navigation, and search. In preliminary work, I have demonstrated that traditional similarity-based methods, particularly network embedding methods, are not readily applicable to complementarity-driven systems [1]. If applied off-the-shelf, these methods may lead to sub-optimal results at best and even lead to wrong conclusions about the system in the worst-case scenario. In this project, I aim to develop a principled theory for the representation of complementarity-driven networks. My preliminary efforts indicate that the thought framework will still be geometric but may involve more complex representations for nodes and links of networks of interest. The project will not only develop the theory of complementarity but also devise computational algorithms to learn complementarity representations of real networks, primarily in domains of Biomedicine and Science of Science.