Random walks are a common model for the exploration and discovery of complex networks. While numerous algorithms have been proposed to map out an unknown network, a complementary question arises: in a known network, which nodes and edges are most likely to be discovered by a random walker in finite time? In this talk we introduce exposure theory, a statistical mechanics framework that predicts the learning of nodes and edges across several types of networks, including weighted and temporal, and show that edge learning follows a universal trajectory. While the learning of individual nodes and edges is noisy, exposure theory produces a highly accurate prediction of aggregate exploration statistics. As a specific application, we extend exposure theory to better understand human learning with its typical mental errors, and thus account for distortions of learned networks.
This talk is based on https://arxiv.org/abs/2202.11262