  Graph energy is the energy of the matrix representation of the graph, where
the energy of a matrix is the sum of singular values of the matrix. Depending
on the definition of a matrix, one can contemplate graph energy, Randi\'c
energy, Laplacian energy, distance energy, and many others. Although
theoretical properties of various graph energies have been investigated in the
past in the areas of mathematics, chemistry, physics, or graph theory, these
explorations have been limited to relatively small graphs representing chemical
compounds or theoretical graph classes with strictly defined properties. In
this paper we investigate the usefulness of the concept of graph energy in the
context of large, complex networks. We show that when graph energies are
applied to local egocentric networks, the values of these energies correlate
strongly with vertex centrality measures. In particular, for some generative
network models graph energies tend to correlate strongly with the betweenness
and the eigencentrality of vertices. As the exact computation of these
centrality measures is expensive and requires global processing of a network,
our research opens the possibility of devising efficient algorithms for the
estimation of these centrality measures based only on local information.
