# Approximate Network Symmetry

In this project, we define a measure of network symmetry that is capable of capturing approximate global symmetries of networks. By applying this measure to networks sampled from several different classic network models, we find that our network symmetry measure can capture properties of network structure. We find that among the network models that we have examined, Erdös-Rényi networks have the lowest levels of symmetry due to their high level of randomness, and Random Geometric Graphs are likely to have a high level of symmetry due to the similarity between nodes embedded in the same regions of space. In addition, we apply the measure to several real-world networks, allowing for us to gain insight into their structure. This work extends previous research on network symmetry by allowing approximate symmetries to be considered, in contrast to previous works that primarily aimed to detect perfect symmetries.

**Publication:**

**Approximate Network Symmetry**. Yanchen Liu. arXiv preprint arXiv:2012.05129 (2020)

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