It is known that the small-world structure constitutes sufficient conditions to sustain cooperation and thus enhances cooperation. On the contrary, the network with a very long average distance is usually thought of as suppressing the emergence of the cooperation. In this paper we show that the fractal structure, of which the average distance is very long, does not always play a negative role in the organization of cooperation. Compared to regular networks, the fractal structure might even facilitate the emergence of cooperation. This mainly depends on the existence of locally compact clusters. The sparse inter-connection between these clusters constructs an asymmetric barrier that the defection strategy is almost impossible to cross, but the cooperation strategy has a not too small chance. More generally, the network need not to be a standard fractal, as long as such structures exist. In turn, when this typical structure is absent, the fractal structure will also suppress the emergence of the cooperation, such as the fractal configuration obtained by diluting a random tree-like network. Our findings also clarify some contradictions in the previous studies, and suggest that both removing and inserting links from/into a regular network can enhance cooperation.

众所周知，小世界结构构成了维持合作并因此加强合作的充分条件。相反，通常认为平均距离非常长的网络会抑制合作的出现。本文表明，平均距离很长的分形结构在合作组织中并不总是起负面作用。与常规网络相比，分形结构甚至可以促进合作的出现。这主要取决于局部紧凑型集群的存在。这些集群之间稀疏的相互联系构成了一个不对称的障碍，叛逃策略几乎是不可能跨越的，但是合作策略的机会却不太小。更普遍，只要存在这样的结构，网络就不必是标准的分形。反过来，当不存在这种典型结构时，分形结构也将抑制协作的出现，例如通过稀释随机树状网络而获得的分形配置。我们的发现还澄清了先前研究中的一些矛盾，并建议从常规网络中删除链接或将链接插入常规网络都可以增强合作。