一种发现和量化复杂网络对称性的严格有效方法
A rigorous and efficient approach to finding and quantifying symmetries in complex networks
摘要：
对称性是复杂网络中动力学过程的基础，如集群同步，这已经吸引了大量的研究。然而，在大型复杂网络中寻找对称节点依赖于代数群论中的自同构群，它们在准多项式时间内是可解的。我们阐明了一个概念上有吸引力的和计算上非常有效的方法，通过引入一个结构位置向量（SPV）的网络中的每个节点，找到和表征所有对称节点。我们从数学上证明了具有相同SPV的节点是相互对称的。利用现实世界中六个典型的复杂网络，证明了所有对称节点都可以在线性时间内找到，SPV不仅可以表征节点的相似性，还可以量化节点对网络传播动力学的影响.我们基于SPV的框架，除了被严格证明，提供了一个物理直观的方式来发现，理解和利用复杂网络中的对称结构。
英文摘要：
Symmetries are fundamental to dynamical processes in complex networks such as cluster synchronization, which have attracted a great deal of current research. Finding symmetric nodes in large complex networks, however, has relied on automorphism groups in algebraic group theory, which are solvable in quasipolynomial time. We articulate a conceptually appealing and computationally extremely efficient approach to finding and characterizing all symmetric nodes by introducing a structural position vector (SPV) for each and every node in the network. We prove mathematically that nodes with the identical SPV are symmetrical to each other. Utilizing six representative complex networks from the real world, we demonstrate that all symmetric nodes can be found in linear time, and the SPVs can not only characterize the similarity of nodes but also quantify the nodal influences in spreading dynamics on the network. Our SPV-based framework, in additional to being rigorously justified, provides a physically intuitive way to uncover, understand and exploit symmetric structures in complex networks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
