中文摘要：

在谱映射的基础上，根据节点到社团的谱映射距离提出了节点的重叠度函数，能够准确地衡量节点与各社团的连接紧密程度，以此得到复杂网络的重叠社团结构。进一步由于经典NG模块度无法衡量重叠社团结构，对表现模块度做了改进，使其不仅能够衡量重叠社团结构的优劣，而且能够应用于现实世界中存在的大量稀疏网络，选择粒度适中的社团结构。最后通过在引文网络和科研合作网络上的应用，与NG模块度和表现模块度对比验证了改进表现模块度和重叠度函数的可行性和有效性。

英文摘要：

Based on the spectral mapping, we define the function of overlapping degree nodes according to the spectral distance between nodes and communities. It can accurately measure the tightness of the nodes between the communities. And we can obtain the overlapping community structure by the function. Further more, we propose the improved performance modularity because NG-modularity can not evaluate the overlapping community structure. The improvement performance modularity not only can evaluate the overlapping community structure, but also can apply in the sparse network that massively exists in the real world. Finally the developed function has been calculated on citation network and coauthorship network. Computational results demonstrate that the proposed the improved modularity and the function of overlapping degree nodes are feasible and effective by comparing with NG-modularity and performance modularity.