Simplification of complex networks by folding

Considering each vertex as a hinge, a network fold method is proposed in this letter. Through continually folding a network, its complexity can be largely reduced, as a result, its kernel or other structural abnormities then can be revealed. It is found that in many real-world networks, large-scale feasible folds are always unpractical, which means the large-scale symmetry-breaking in these networks. It seems that such large-scale symmetry breaking may be caused by the random growth of these networks, because, different from the initial networks, their revealed kernels present surprisingly large-scale symmetric structures. Such inconsistency may be avoided by providing a new definition of statistical symmetry for networks in the future.