Detection of non-overlapping and overlapping communities are essentially the same problem. However, current algorithms focus either on finding overlapping or non-overlapping communities. We present a generalized framework that can identify both non-overlapping and overlapping communities, without any prior input about the network or its community distribution. To do so, we introduce a vertex-based metric, GenPerm , that quantifies by how much a vertex belongs to each of its constituent communities. Our community detection algorithm is based on maximizing the GenPerm over all the vertices in the network. We demonstrate, through experiments over synthetic and real-world networks, that GenPerm is more effective than other metrics in evaluating community structure. Further, we show that due to its vertex-centric property, GenPerm can be used to unfold several inferences beyond community detection, such as core-periphery analysis and message spreading. Our algorithm for maximizing GenPerm outperforms six state-of-the-art algorithms in accurately predicting the ground-truth labels. Finally, we discuss the problem of resolution limit in overlapping communities and demonstrate that maximizing GenPerm can mitigate this problem.
There has been a class of algorithms for network clustering, which allow nodes belonging to more than one community. Palla proposed CFinder'' @cite_28 , the seminal and most popular method based on clique-percolation technique. However, due to the clique requirement and the sparseness of real networks, the communities discovered by CFinder are usually of low quality @cite_1 . The idea of partitioning links instead of nodes to discover community structure has also been explored @cite_42
@cite_28 @cite_42 @cite_1
2146659008 2963315742 1976160665 2033507223
The inclusion of link weights into the analysis of network properties allows a deeper insight into the (often overlapping) modular structure of real- world webs. We introduce a clustering algorithm clique percolation method with weights (CPMw) for weighted networks based on the concept of percolating k-cliques with high enough intensity. The algorithm allows overlaps between the modules. First, we give detailed analytical and numerical results about the critical point of weighted k-clique percolation on (weighted) Erdý os-Renyi graphs. Then, for a scientist collaboration web and a stock correlation graph we compute three-link weight correlations and with the CPMw the weighted modules. After reshuffling link weights in both networks and computing the same quantities for the randomized control graphs as well, we show that groups of three or more strong links prefer to cluster together in both original graphs. Abstract Community structure is one of the most prominent features of complex networks. Community structure detection is of great importance to provide insights into the network structure and functionalities. Most proposals focus on static networks. However, finding communities in a dynamic network is even more challenging, especially when communities overlap with each other. In this article, we present an online algorithm, called OLCPM, based on clique percolation and label propagation methods. OLCPM can detect overlapping communities and works on temporal networks with a fine granularity. By locally updating the community structure, OLCPM delivers significant improvement in running time compared with previous clique percolation techniques. The experimental results on both synthetic and real-world networks illustrate the effectiveness of the method. Graph clustering has been widely applied in exploring regularities emerging in relational data. Recently, the rapid development of network theory correlates graph clustering with the detection of community structure, a common and important topological characteristic of networks. Most existing methods investigate the community structure at a single topological scale. However, as shown by empirical studies, the community structure of real world networks often exhibits multiple topological descriptions, corresponding to the clustering at different resolutions. Furthermore, the detection of multiscale community structure is heavily affected by the heterogeneous distribution of node degree. It is very challenging to detect multiscale community structure in heterogeneous networks. In this paper, we propose a novel, unified framework for detecting community structure from the perspective of dimensionality reduction. Based on the framework, we first prove that the well-known Laplacian matrix for network partition and the widely-used modularity matrix for community detection are two kinds of covariance matrices used in dimensionality reduction. We then propose a novel method to detect communities at multiple topological scales within our framework. We further show that existing algorithms fail to deal with heterogeneous node degrees. We develop a novel method to handle heterogeneity of networks by introducing a rescaling transformation into the covariance matrices in our framework. Extensive tests on real world and artificial networks demonstrate that the proposed correlation matrices significantly outperform Laplacian and modularity matrices in terms of their ability to identify multiscale community structure in heterogeneous networks. It has been shown that the communities of complex networks often overlap with each other. However, there is no effective method to quantify the overlapping community structure. In this paper, we propose a metric to address this problem. Instead of assuming that one node can only belong to one community, our metric assumes that a maximal clique only belongs to one community. In this way, the overlaps between communities are allowed. To identify the overlapping community structure, we construct a maximal clique network from the original network, and prove that the optimization of our metric on the original network is equivalent to the optimization of Newman's modularity on the maximal clique network. Thus the overlapping community structure can be identified through partitioning the maximal clique network using any modularity optimization method. The effectiveness of our metric is demonstrated by extensive tests on both artificial networks and real world networks with a known community structure. The application to the word association network also reproduces excellent results.