Recent studies revealed an important interplay between the detailed structure of fibration symmetric circuits and the functionality of biological and non-biological networks within which they have be identified. The presence of these circuits in complex networks are directed related to the phenomenon of cluster synchronization, which produces patterns of synchronized group of nodes. Here we present a fast, and memory efficient, algorithm to identify fibration symmetries over information-processing networks. This algorithm is specially suitable for large and sparse networks since it has runtime of complexity $O(M\log N)$ and requires $O(M+N)$ of memory resources, where $N$ and $M$ are the number of nodes and edges in the network, respectively. We propose a modification on the so-called refinement paradigm to identify circuits symmetrical to information flow (i.e., fibers) by finding the coarsest refinement partition over the network. Finally, we show that the presented algorithm provides an optimal procedure for identifying fibers, overcoming the current approaches used in the literature.

翻译：最近的研究揭示了纤维化对称电路的详细结构与生物和非生物网络的功能之间的重要相互作用。这些电路在复杂网络中的存在与集束同步现象有关,即产生同步节点组合的模式。这里我们提出了一个快速和记忆效率的算法,用以查明信息处理网络上的纤维化对称。这一算法特别适合大型和稀疏网络,因为其运行时间很复杂(M\log N)美元,需要(M+N)美元记忆资源,其中美元和美元是网络中的节点和边缘。我们建议修改所谓的精细模式,通过在网络上找到粗糙的精密分区,确定对信息流动(即纤维)的对称。最后,我们表明,所提出的算法为识别纤维提供了最佳程序,克服了文献中目前使用的方法。