The inducibility of graphs

Abstract We investigate the maximum number of ways in which a k -vertex graph G can appear as an induced subgraph of an n -vertex graph, for n ≥ k . When this number is expressed as a fraction of all k -vertex induced subgraphs, it tends to a definite limit as n → ∞. This limit, which we call the inducibility of G , is an effectively computable invariant of G . We examine the elementary properties of this invariant: its relationship to various operations on graphs, its maximum and minimum values, and its value for some particular graphs.