递归网络能显示小世界性质吗？
Can recurrence networks show small world property?
摘要：
递归网络是由时间序列数据构建的复杂网络，具有多种实际应用。虽然当阈值ε等于或略高于网络的逾渗阈值时，它们的性质已经很好地理解了，但从复杂网络的角度来看，当阈值增加超过通常的操作窗口时会发生什么仍然不清楚。这封信主要集中在复发阈值的中到大值的网络属性，迄今为止还没有进行系统的研究。我们认为，与数值支持，递归网络构造的混沌吸引子与ε等于或略高于通常的递归阈值，在一般情况下，不能表现出小世界性质。然而，如果阈值进一步增加，递归网络的拓扑结构最初改变为一个小世界结构，并最终为一个经典的随机图的阈值接近的大小的奇异吸引子。
英文摘要：
Recurrence networks are complex networks, constructed from time series data, having several practical applications. Though their properties when constructed with the threshold value εchosen at or just above the percolation threshold of the network are quite well understood, what happens as the threshold increases beyond the usual operational window is still not clear from a complex network perspective. The present Letter is focused mainly on the network properties at intermediate-to-large values of the recurrence threshold, for which no systematic study has been performed so far. We argue, with numerical support, that recurrence networks constructed from chaotic attractors with εequal to the usual recurrence threshold or slightly above cannot, in general, show small-world property. However, if the threshold is further increased, the recurrence network topology initially changes to a small-worldstructure and finally to that of a classical random graph as the threshold approaches the size of the strange attractor.
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