Measuring and characterizing complex networks is a hard problem simply because of the enormous variety of relevant metrics that apply to particular classes of complex network. No one metric is universally useful, therefore it is necessary to consider the interplay and ranges of applicability of several metrics. Not all metrics are simply computed, with some being $O(n)$ and others having a considerably worse computational cost. This article presents some metrics, algorithms for their evaluation, and some illustrative examples of the regimes in which they are useful. Particular focus is given to asymmetric networks and cases where the eigenvalues of the network's adjacency matrix are potentially complex numbers. Some results on the density spectrum of the eigenvalues are presented and discussed in the context of histograms over the complex plane.
Keywords: complexity; complexity measures; complex systems; complex eigenvalues.
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