A fibration of graphs is an homomorphism that is a local isomorphism of in-neighbourhoods, much in the same way a covering projection is a local isomorphism of neighbourhoods. Recently, it has been shown that graph fibrations are useful tools to uncover symmetries and synchronization patterns in biological networks ranging from gene, protein,and metabolic networks to the brain. However, the inherent incompleteness and disordered nature of biological data precludes the application of the definition of fibration as it is; as a consequence, also the currently known algorithms to identify fibrations fail in these domains. In this paper, we introduce and develop systematically the theory of quasifibrations which attempts to capture more realistic patterns of almost-synchronization of units in biological networks. We provide an algorithmic solution to the problem of finding quasifibrations in networks where the existence of missing links and variability across samples preclude the identification of perfect symmetries in the connectivity structure. We test the algorithm against other strategies to repair missing links in incomplete networks using real connectome data and synthetic networks. Quasifibrations can be applied to reconstruct any incomplete network structure characterized by underlying symmetries and almost synchronized clusters.

翻译：图表的纤维化是一种同质论,它是一种地方性邻居的异形,其结果是,目前已知的用来识别这些域内的纤维化失灵的算法。在本文件中,我们提出并系统地发展准纤维化理论,试图捕捉生物网络中单位几乎同步化的更为现实的模式。我们为在网络中寻找从基因、蛋白质和代谢网络到大脑的准结构的问题提供了一种算法解决办法。在网络中,由于缺少联系和样本的变异性,无法确定连接结构中的完美对称性。我们用实际连接数据和合成网络来测试其他方法,以修复不完整网络中缺失的链接。通过不完全的网络结构,可以进行不完全的同步的网络结构。