This paper introduces a method to analyze the overlapping community structure in complex networks, which is crucial for understanding the functional and structural properties of networks. Existing methods often identify separated communities, but many real networks consist of highly overlapping communities. The authors propose a new approach to analyze the statistical features of overlapping communities, leading to a better understanding of the modular structure of complex systems. The method defines new characteristic quantities for community statistics, such as community size, community degree, overlap size, and membership number. These quantities are used to analyze the structure of communities in various networks, including collaboration networks, word association networks, and protein interaction networks. The results show that communities in these networks have non-trivial correlations and specific scaling properties. The authors define a community as a set of overlapping k-clique communities, where a k-clique is a complete subgraph of size k. This definition allows for the identification of communities that are highly connected and share many nodes. The method is applied to three large networks: a co-authorship network, a word association network, and a protein interaction network. The results show that the communities identified by this method have significant overlaps and are more accurate than traditional methods. The paper also discusses the statistical properties of the communities, including the distribution of community sizes, community degrees, overlap sizes, and membership numbers. These distributions reveal universal features of networks and show that the community structure of real networks is more complex than previously thought. The authors conclude that their method provides a more accurate and comprehensive way to analyze the community structure of complex networks. This method has potential applications in various fields, including biology, sociology, and computer science. The results demonstrate that the community structure of real networks is more complex and has specific scaling properties, which can be used to predict the behavior of complex systems.This paper introduces a method to analyze the overlapping community structure in complex networks, which is crucial for understanding the functional and structural properties of networks. Existing methods often identify separated communities, but many real networks consist of highly overlapping communities. The authors propose a new approach to analyze the statistical features of overlapping communities, leading to a better understanding of the modular structure of complex systems. The method defines new characteristic quantities for community statistics, such as community size, community degree, overlap size, and membership number. These quantities are used to analyze the structure of communities in various networks, including collaboration networks, word association networks, and protein interaction networks. The results show that communities in these networks have non-trivial correlations and specific scaling properties. The authors define a community as a set of overlapping k-clique communities, where a k-clique is a complete subgraph of size k. This definition allows for the identification of communities that are highly connected and share many nodes. The method is applied to three large networks: a co-authorship network, a word association network, and a protein interaction network. The results show that the communities identified by this method have significant overlaps and are more accurate than traditional methods. The paper also discusses the statistical properties of the communities, including the distribution of community sizes, community degrees, overlap sizes, and membership numbers. These distributions reveal universal features of networks and show that the community structure of real networks is more complex than previously thought. The authors conclude that their method provides a more accurate and comprehensive way to analyze the community structure of complex networks. This method has potential applications in various fields, including biology, sociology, and computer science. The results demonstrate that the community structure of real networks is more complex and has specific scaling properties, which can be used to predict the behavior of complex systems.