Rado constructed a (simple) denumerable graph \( R \) with the positive integers as vertex set with the following edges: For given \( m \) and \( n \) with \( m < n \), \( m \) is adjacent to \( n \) if \( n \) has a \( 1 \) in the \( m \)'th position of its binary expansion. It is well known that \( R \) is a universal graph in the set \( \mathcal{I} \) of all countable graphs (since every graph in \( \mathcal{I} \) is isomorphic to an induced subgraph of \( R \)) and that \( R \) can be characterized using this notion and that of being homogeneous and having the extension property. In this paper, we extend these notions to arbitrary induced-hereditary properties (of graphs), relate them to the construction of a universal graph for any such property, and obtain results which remind one of some characterizations of \( R \).