The chemical and physical properties of nanoclusters largely depend on their sizes and shapes.
This is partly due to finite size effects influencing the local electronic structure of the
nanocluster atoms which are located on the nanofacets and on their edges. Here we present a
thorough study on graphene-supported Rh nanocluster assemblies and their geometrydependent
electronic structure obtained by combining high-energy resolution core level
photoelectron spectroscopy, scanning tunneling microscopy, and density functional theory. We
demonstrate the possibility to finely control the morphology and the degree of structural order
of Rh clusters grown in register with the template surface of graphene/Ir(111). By comparing
measured and calculated core electron binding energies, we identify edge, facet, and bulk
atoms of the nanoclusters. We describe how small interatomic distance changes occur while
varying the nanocluster size, substantially modifying the properties of surface atoms. The
properties of under-coordinated Rh atoms are discussed in view of their importance in
heterogeneous catalysis and magnetism.