中文摘要：

很多现实的复杂网络都具有无标度特性，其节点度具有幂律分布的规律。主要讨论幂指数γ〈2的无标度网络的性质，指出当γ〈2时，网络中最小度的节点数以及网络的平均度都与网络大小N有某种数量关系。通过与γ≥2的无标度网络对比，该类特殊网络呈现出不同的性质和行为，网络的边与节点相比呈现快速增长，具有更大的平均度，网络中有更多的边，网络不再稀疏。

英文摘要：

Many complex networks exhibit a scale-free property, with power-law vertex degree. This common feature consequents from the two generic mechanisms relating to the formation of real networks：expansion and preferential attachment. In this paper we mainly discussed the properties of scale-free networks with the exponent γ〈2. We showed that when γ〈2,the number of min-degree vertices and the average degree had some quantitative relationship with the network size N. Compared with scale-free networks with , we found that these special type of networks exhibited different properties and behaviors.