  Virtually all network analyses involve structural measures between pairs of
vertices, or of the vertices themselves, and the large amount of symmetry
present in real-world complex networks is inherited by such measures. This has
practical consequences which have not yet been explored in full generality, nor
systematically exploited by network practitioners. Here we study the effect of
network symmetry on arbitrary network measures, and show how this can be
exploited in practice in a number of ways, from redundancy compression, to
computational reduction. We also uncover the spectral signatures of symmetry
for an arbitrary network measure such as the graph Laplacian. Computing network
symmetries is very efficient in practice, and we test real-world examples up to
several million nodes. Since network models are ubiquitous in the Applied
Sciences, and typically contain a large degree of structural redundancy, our
results are not only significant, but widely applicable.
