Universal lossless compression of graphical data

Consider a data source comprised of a graph with marks on its edges and vertices. Examples of such data sources are social networks, biological data, web graphs, etc. Our goal is to design schemes that can efficiently compress and store such data. We aim for universal compression, i.e. without making assumptions about the stochastic properties of the data. To make sense of this, we employ the framework of local weak convergence, also called the objective method, which formalizes the notion of stationary stochastic processes indexed by graphs. We generalize a recently developed notion of entropy for such processes, due to Bordenave and Caputo, to the case of marked graphs, and argue that it is an appropriate way to evaluate the efficiency of a compression scheme. The lossless compression scheme we propose in this paper is then proved to be universally optimal. It is also capable of performing local data queries in the compressed form.