In the formalism that separates bonds into σ and π types, hyperconjugation is the interaction of σ-bonds (e.g. C-H, C-C, etc.) with a π network.
This interaction is customarily illustrated by contributing structures, e.g. for toluene (below), sometimes said to be an example of "heterovalent" or "sacrificial hyperconjugation", so named because the contributing structure contains one two-electron bond less than the normal Lewis formula for toluene.
The concept of hyperconjugation is also applied to carbenium ions and radicals, where the interaction is now between σ-bonds and an unfilled or partially filled π or p-orbital. A contributing structure illustrating this for the tert-butyl cation is:
This latter example is sometimes called an example of "isovalent hyperconjugation" (the contributing structure containing the same number of two-electron bonds as the normal Lewis formula).
Both structures are also examples of "double bond- no-bond resonance".