We introduce network science as a framework for studying the string landscape. Two large networks of string geometries are constructed, where nodes are extra-dimensional six-manifolds and edges represent topological transitions between them. We show that a standard bubble cosmology model on the networks has late-time behavior determined by the largest eigenvector of -(L+D), where L and D are the Laplacian and degree matrices of the networks, which provides a dynamical mechanism for vacuum selection in the string landscape.