ENTROPY AND THE COMPLEXITY OF GRAPHS: II. THE INFORMATION CONTENT OF DIGRAPHS AND INFINITE GRAPHS

of the structural information content of an (undirected) graph X was defined, and its properties explored. The class of graphs on which Ig is defined is here enlarged to include directed graphs (digraphs). Most of the properties of I 0 observed in the undirected case are seen to hold for digraphs. The greater generality of digraphs allows for a construction which shows that there exists a digraph having information content equal to the entropy of an arbitrary partition of a given positive integer. The measure Ig is also extended to a measure defined on infinite (undirected) graphs. The properties of this extension are discussed, and its applicability to the problem of measuring the complexity of algorithms is considered.