Molecules can be regarded as a kind of graph with atoms as vertices and bonds as edges. Therefore, it is possible to discuss the physical properties and reactivity of various molecules by applying the ideas of graph theory and network theory. Such research has flourished in the field of chemical graph theory. In this manuscript, it is shown that the lowest occupied molecular orbital (LOMO) can be interpreted graph theoretically as eigenvector centrality. This is one measure of centrality that characterizes the importance or influence of a node on a network. As such, LOMO coefficient can be regarded as a manifestation of centrality in an aggregate of atoms, indicating which atom plays the most important role in that aggregate or has the greatest influence on the atom network. Using such properties of LOMO, an analysis of the network of metal atoms in metal clusters is performed. The predictability of the binding energies of the constituent atoms of the metal clusters using LOMO coefficients is discussed.
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