  There are different measures to classify a network's data set that, depending
on the problem, have different success. For example, the resistance distance
and eigenvector centrality measures have been successful in revealing
ecological pathways and differentiating between biomedical images of patients
with Alzheimer's disease, respectively. The resistance distance measures the
effective distance between any two nodes of a network taking into account all
possible shortest paths between them and the eigenvector centrality measures
the relative importance of each node in the network. However, both measures
require knowing the network's eigenvalues and eigenvectors -- eigenvectors
being the more computationally demanding task. Here, we show that we can
closely approximate these two measures using only the eigenvalue spectra, where
we illustrate this by experimenting on elemental resistor circuits and
paradigmatic network models -- random and small-world networks. Our results are
supported by analytical derivations, showing that the eigenvector centrality
can be perfectly matched in all cases whilst the resistance distance can be
closely approximated. Our underlying approach is based on the work by Denton,
Parke, Tao, and Zhang [arXiv:1908.03795 (2019)], which is unrestricted to these
topological measures and can be applied to most problems requiring the
calculation of eigenvectors.
