Efficient coding of labelled graphs

The efficient coding of directed graphs can be of importance in data compression algorithms, as well as in graphical modelling applications in artificial intelligence and biological network reconstruction. One type of code commonly used involves the separate coding of node parent sets, and can be shown to have an asymptotic code length proportional to the number of edges. We show the existence of an alternative code, based on graph blocks, which can be shown to be of uniformly shorter length under asymptotically invariant conditions.