In the field of community detection in complex networks, the most commonly used approach to this problem is the maximization of the benefit function known as “modularity”. In this study, it is found that the path of length two have the similar property as the edge, which is denser within communities and sparser between different communities. In order to take both edge and path of length two into consideration simultaneously, a self-loop is added to each node of the network and a novel benefit function has been defined. To divide the network into two communities, a second eigenvector method is proposed based on maximization of our new benefit function. Experimental results obtained by applying the method to karate club network and dolphin social network show the feasibility of our benefit function and the effectiveness of our algorithm.

中文翻译：

---

基于长度为2的边和路径的社区检测收益函数

在复杂网络中的社区检测领域，解决这个问题最常用的方法是最大化收益函数，称为“模块化”。在本研究中，发现长度为 2 的路径具有与边相似的性质，在社区内更密集，在不同社区之间更稀疏。为了同时考虑长度为 2 的边和路径，网络的每个节点都添加了一个自环，并定义了一个新的收益函数。为了将网络划分为两个社区，在最大化我们的新收益函数的基础上，提出了第二种特征向量方法。将该方法应用于空手道俱乐部网络和海豚社交网络的实验结果表明了我们的收益函数的可行性和算法的有效性。