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 that 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.

实际上，所有网络分析都涉及成对的顶点之间或顶点本身之间的结构度量，并且在现实世界中复杂网络中存在的大量对称性是由此类度量继承的。这具有实际的后果，尚未全面探讨，也没有被网络从业人员系统地利用。在这里，我们研究了网络对称性对任意网络度量的影响，并展示了如何在实践中以多种方式利用这一点，从冗余压缩到计算约简。我们还发现了任意网络度量（例如图拉普拉斯算子）的对称性的光谱特征。在实践中，计算网络对称性非常有效，我们可以测试多达数百万个节点的实际示例。由于网络模型在应用科学中无处不在，