Strictly balanced graph ($e(F)/v(F)<e(H)/v(H)$)

A finite graph $H$ with at least one edge is strictly balanced when every proper nonempty subgraph $F$ has smaller edge-to-vertex ratio. It is connected and has no isolated vertices: otherwise a component of at least the average density, or deletion of isolated vertices, violates the inequality. The density condition suppresses overlapping copies at the sparse appearance scale.