We propose a new method for the classification of excitations of nuclei. Taking 12C as an example, we determine whether a given excited state is more of an 𝛼-cluster excitation or a single-nucleon
excitation. Using the so-called pinhole algorithm in the framework of nuclear lattice effective field theory, we study the distance between any two 𝛼 clusters in the nucleus, and the separations of
arbitrarily chosen nucleons inside an 𝛼 cluster. For a state which is predominantly a cluster-type excitation (such as the Hoyle state) the distribution of 𝛼 − 𝛼 separations is very different from that
of the ground state. For states that are predominantly single-nucleon excitations, the two-nucleon separation inside an 𝛼 cluster is in general increased.