The emergence of differences in the arrangement of cells is the first step towards the establishment of many organs. Understanding this process is limited by the lack of systematic characterization of epithelial organisation. Here we apply network theory at the scale of individual cells to uncover patterns in cell-to-cell contacts that govern epithelial organisation. We provide an objective characterisation of epithelia using network representation, where cells are nodes and cell contacts are links. The features of individual cells, together with attributes of the cellular network, produce a defining signature that distinguishes epithelia from different organs, species, developmental stages and genetic conditions. The approach permits characterization, quantification and classification of normal and perturbed epithelia, and establishes a framework for understanding molecular mechanisms that underpin the architecture of complex tissues.