Component-trees are classical tree structures for grey-level image modelling. Component-graphs are defined as a generalization of component-trees to images taking their values in any (totally or partially) ordered sets. Similarly to component-trees, component-graphs are a lossless image model; then, they can allow for the development of various image processing approaches. However, component-graphs are not trees, but directed acyclic graphs. This makes their construction non-trivial, leading to non-linear time cost and resulting in non-linear space data structures. In this theoretical article, we discuss the notion(s) of component-graph, and we propose a strategy for their efficient building and representation, which are necessary conditions for further involving them in image processing approaches.