Many real-world networks have high clustering among vertices: vertices that share neighbors are often also directly connected to each other. A network's clustering can be a useful indicator of its connectedness and community structure. Algorithms for generating networks with high clustering have been developed, but typically rely on adding or removing edges and nodes, sometimes from a completely empty network. Here, we introduce algorithms that create a highly clustered network by starting with an existing network and rearranging edges, without adding or removing them; these algorithms can preserve other network properties even as the clustering increases. They rely on local rewiring rules, in which a single edge changes one of its vertices in a way that is guaranteed to increase clustering. This greedy step can be applied iteratively to transform a random network into a form with much higher clustering. Additionally, the algorithms presented grow a network's clustering faster than they increase its path length, meaning that network enters a regime of comparatively high clustering and low path length: a small world. These algorithms may be a basis for how real-world networks rearrange themselves organically to achieve or maintain high clustering and small-world structure.
Critical behavior and correlations on scale-free small-world networks. Application to network design
我们分析的关键现象产生的网络作为联盟的隐变量模型（网络与任何所需的程度序列）与任意图形。由此产生的网络是一般的小世界，类似于a` la Watts和Strogatz，但具有异质度分布。我们证明了临界行为（热或热）保持完全不变的有限循环（或有限集群）的存在。然后，我们表明，在大但有限的网络中，两个给定的自旋的相关性可能很强，即，在任何温度下都近似于幂律。非常有趣的是，如果$γ$是顶点度的幂律分布的指数，那么对于$γ\leq 3$，无论有没有短程耦合，这种强相关性甚至在热力学极限下都持续存在，这与平均场模型中相关性总是在此极限下消失的普遍观点相矛盾。最后，我们提供了最佳的选择重新布线下，在重新布线的网络中的渗流现象是最好的执行;一个自然的标准，以达到最佳的通信功能，至少在非拥塞的制度。
