A graph composed of nodes and edges may be an abstr action of a software system and a sub graph may represent a software module. Software-design graphs depict components and their relationships. Building on prior work by Allen, Khoshgoftaar, and Chen, this paper proposes information theory-based measures on graphs at the system and module levels for application to software. We propose measures of size, length, complexity, coupling, and cohesion which largely conform to the properties of these attributes defined by Briand, Morasca, and Basili. We illustrate the measures with examples and suggest extensions for hypergraphs.