Network Fundamentals
Network geometry
Discovering latent geometry driving network evolution

Heterogeneous degree distributions and strong clustering observed in many real networks imply that these networks have a latent geometric structure. In other words, real networks can be viewed as certain discretizations of smooth geometric spaces: network nodes are points in these spaces and the probability of a connection between any two nodes is a decreasing function of the distance between the nodes in the space. We want to understand how latent geometry shapes topological properties of evolving networks and to devise efficient methods to uncover latent geometries of real networks. Geometric methods have proven to be extremely useful in predicting missing and future links, developing better recommendation systems, estimating biases associated with incomplete data, identification of disease mechanisms, understanding human communication patterns, and signaling in the brain.