Abstract: In most real-world networks, there are no completely independent community structures, and they are usually made up of many intertwined and overlapping communities. An overlapping community structure refers to nodes that can belong to multiple different communities at the same time. For example, in a scientific collaboration network, some scientists may be both biologists and mathematicians. If we classify this network according to different disciplines, the same individual may be assigned to two different communities. In university student associations, some students participate in multiple associations, so as to be categorized into various communities. University student associations have the following characteristics: First, there are many organizations with a wide variety and large number of participants. Second, associations are becoming increasingly diverse. Different students' interests and hobbies are quite different, forming a wide range of university associations. Third, each organization establishes its own rules and regulations, with a more systematic management approach. The overlapping structures within university student associations represent the cross-penetration between communities. Studying the cross-penetration of university organizations from the perspective of the overlapping structure is a worthwhile topic to explore.
Based on this, this paper collects a total of 6,580 data points on university students' participation in associations through surveys, QR code scanning, and hyperlinks. It removes responses from individuals who do not participate in any associations and those who have no common associations with any classmates, resulting in 5,040 valid data points. Each university student is treated as a node, and since students within the same organization know each other, a fully connected network of nodes belonging to the same organization is formed, creating edges for the network and constructing the university organization network. Using the k-clique percolation algorithm, we perform the overlapping structure detection and community partitioning. Furthermore, based on different values of k, we analyze overlapping relationships within the network by combining certain metrics of complex networks and hypernetworks.
By comparing the ratio of retained nodes, number of community partition, and modularity Q value across different values of k to the actual partition results from the empirical dataset, the effectiveness of the algorithm is validated, leading to the optimal value of k. This paper helps to analyze the structure and characteristics of university associations, further puts forward guiding suggestions for the construction of associations in three aspects, namely, attaching importance to the guiding role of schools, strengthening the construction of association talents and association culture, and avoiding blind obedience in joining associations, which provide a theoretical basis for the construction and service of university associations and the selection of associations by college students, and also has certain practical significance.
In future research, we will combine the characteristics of overlapping communities to find a fast and reliable community detection algorithm, and focus on the community detection method for hypergraph to ensure the practicability of the method. In addition, this paper studies the static undirected unweighted network, but due to the network evolution of new nodes and the new relationship, makes the network as a whole in a dynamic change. There are some directional edges in the real network, so there are a lot of weighted and directed networks. How to extend the community detection method to these networks is also the next research direction.

Key words: overlapping structure, university associations, k-clique percolation algorithm, complex network, hypernetwork

摘要： 高校学生社团中的重叠结构代表社团之间的交叉渗透,从重叠结构的角度研究高校社团之间的交叉渗透是一个值得探索的问题。本文以在校学生为节点,同一社团内的学生相互连接为边,构建高校社团网络,利用k-派系过滤算法实现重叠结构检测及社团的划分,并在此基础上,结合k的不同取值、复杂网络以及超网络的部分指标进一步分析网络中的重叠关系。通过将k取不同值时未丢失节点数量的比值、社团划分数量和模块度Q值与高校社团实证数据集的实际划分结果进行对比分析,验证了该算法的有效性,得到了k的最佳取值。本文有助于分析高校社团的结构、特点,进一步,分别从重视学校的引导作用、加强社团人才文化建设、参加社团避免盲从这三方面提出了社团建设的指导性建议,为高校社团的建设及大学生选择社团提供了理论依据,且具有一定的现实意义。

关键词: 重叠结构, 高校社团, k-派系过滤算法, 复杂网络, 超网络