A Transformative Topological Representation for Link Modeling, Prediction and Cross-Domain Network Analysis.

Many complex social, biological, or physical systems are characterized as networks, and recovering the missing links of a network could shed important lights on its structure and dynamics. A good topological representation is crucial to accurate link modeling and prediction, yet how to account for the kaleidoscopic changes in link formation patterns remains a challenge, especially for analysis in cross-domain studies. We propose a new link representation scheme by projecting the local environment of a link into a "dipole plane", where neighboring nodes of the link are positioned via their relative proximity to the two anchors of the link, like a dipole. By doing this, complex and discrete topology arising from link formation is turned to differentiable point-cloud distribution, opening up new possibilities for topological feature-engineering with desired expressiveness, interpretability and generalization. Our approach has comparable or even superior results against state-of-the-art GNNs, meanwhile with a model up to hundreds of times smaller and running much faster. Furthermore, it provides a universal platform to systematically profile, study, and compare link-patterns from miscellaneous real-world networks. This allows building a global link-pattern atlas, based on which we have uncovered interesting common patterns of link formation, i.e., the bridge-style, the radiation-style, and the community-style across a wide collection of networks with highly different nature.