基于动态演化博弈的复杂网络社区检测

Recent years, complex network has attracted many scholars, among which community structure and dynamic behaviors are more active. Community detection is very important to analyze the structure and nature of the network. The dynamic evolutionary game of the nodes in networks is adopted to detect community structure in our project. The main contribution is several efficient community detection algorithms for real networks are presented by using the fact that community structure affects the dynamic behaviors, and dynamic behaviors meanly show the community structure. Firstly, we establish a static weighted overlapping network model corresponding to the influence of the different weights on the dynamical evolutionary behaviors. Here, the nodes in the same community will own the same profits and the nodes in the different community will tend to obtain different profits. Now, the community structure is obvious. Secondly, a dynamic weighted overlapping network model is given according to the characteristics of real networks. It is noted that the replicated dynamic equations of dynamic evolutionary game is improved according to the characters of the networks. Thus, the community structure of the networks will be detected when the nodes are evolving based on the improved replicated dynamic equations. We will further analyze the influence of the parameters on the speed and accuracy, and then compare the advantages of the popular community detection algorithms with ours. The algorithms proposed in this project have no use for any prior information and they have less calculation, which are more attractive in the applications in real networks. The community detection algorithms in our project will present a novel idea for the combination of dynamic evolutionary game and community detection.

复杂网络的研究近年来吸引了许多学者，其中社区检测和动力学行为是目前的研究热点。揭示网络的社区结构，对深入了解网络结构、分析网络特性是非常关键的。本项目拟利用节点的动态演化博弈来检测社区结构。首先，基于演化动力学行为反映社区结构，建立加权重叠网络模型，并利用动态演化博弈所得出的节点分组结果进行静态社区检测。然后，针对复杂网络的动态拓扑结构，结合复制动态方程建立网络模型，给出动态社区检测算法。需要指出的是，本项目中算法将动态演化博弈中的复制动态方程针对社区检测具体情形做出相应改进，使得网络节点按照改进的复制动态方程演化时出现分组，进而发现社区。同时讨论模型中相关参数对检测速度、精度的影响，与目前公认算法比较优缺点，项目所提出的算法不需要社区结构的先验信息并且节点演化的计算量相对要小，更适应于大规模的真实网络。我们所提出的社区检测算法会对以后进一步将动态演化博弈与社区检测有效结合提供新思路。

本项目根据拟定的研究计划，主要利用节点动态演化所体现出来的状态稳定结果来检测社区结构。具体研究成果如下: 1.针对复杂网络的拓扑结构进行数据分析，定义了基于模块度矩阵的节点相似度。给出网络模型得出两个社区检测算法并对合成网络和真实网络作相关的数值仿真实验取得较好效果。2.针对符号网络的社区检测问题，根据节点间的共性和差异性定义相似度。给出一种基于动态演化的符号网络社区检测方法，克服了现有技术检测效率低、复杂度高的缺陷。对合成网络和真实网络进行了数值仿真实验，取得较好的社区划分效果。3.结合动态演化博弈的思想，给出快速有效的无线认知网络中频谱分配算法和异质网络选择算法。我们给出一个改进的复制动力学方程，该方程只需要网络节点的邻居信息，自适应地收敛到预期的稳定状态，速度更快。4.将基于Hamilton算子的分离变量法应用到点群12mm十二次对称准晶平面弹性问题。这是无穷维Hamilton算子应用到准晶平面弹性问题的初次尝试，并得到了比较好的效果。目前工作已按计划圆满完成。发表论文3篇（其中SCI两篇），申请发明专利一项。本项目所提出的算法不需要社区结构的先验信息并且节点演化的计算量相对较小，与相关算法做比较具有一定优势，特别是我们的社区检测算法对后续进一步将动力学行为分析与社区检测有效结合提供了新思路。