Evidential Communities for Complex Networks

Community detection is of great importance for understand-ing graph structure in social networks. The communities in real-world networks are often overlapped, i.e. some nodes may be a member of multiple clusters. How to uncover the overlapping communities/clusters in a complex network is a general problem in data mining of network data sets. In this paper, a novel algorithm to identify overlapping communi-ties in complex networks by a combination of an evidential modularity function, a spectral mapping method and evidential c-means clustering is devised. Experimental results indicate that this detection approach can take advantage of the theory of belief functions, and preforms good both at detecting community structure and determining the appropri-ate number of clusters. Moreover, the credal partition obtained by the proposed method could give us a deeper insight into the graph structure

Overlapping Community Detection using Local Seed Expansion

Communities are usually groups of vertices which have higher probability of being connected to each other than to members of other groups. Community detection in complex networks is one of the most popular topics in social network analysis. While in real networks, a person can be overlapped in multiple communities such as family, friends and colleagues, so overlapping community detection attracts   more and more attention.  Detecting communities from the local structural information of a small number of seed nodes is the successful methods for overlapping community detection. In this work, we propose an overlapping community detection algorithm using local seed expansion approach. Our local seed expansion algorithm selects the nodes with the highest degree as seed nodes and then locally expand these seeds with their entire vertex neighborhood into overlapping communities using Personalized PageRank algorithm. We use F1_score( node  level detection )  and NMI( community level detection ) measures to assess the performances of the proposed algorithm by comparing the proposed algorithm’s detected communities with ground_truth communities on many real_world networks. Experimental results show that our algorithm outperforms over other overlapping community detection methods in terms of accuracy and quality of overlapped communities

A maximal clique based multiobjective evolutionary algorithm for overlapping community detection

Detecting community structure has become one im-portant technique for studying complex networks. Although many community detection algorithms have been proposed, most of them focus on separated communities, where each node can be-long to only one community. However, in many real-world net-works, communities are often overlapped with each other. De-veloping overlapping community detection algorithms thus be-comes necessary. Along this avenue, this paper proposes a maxi-mal clique based multiobjective evolutionary algorithm for over-lapping community detection. In this algorithm, a new represen-tation scheme based on the introduced maximal-clique graph is presented. Since the maximal-clique graph is defined by using a set of maximal cliques of original graph as nodes and two maximal cliques are allowed to share the same nodes of the original graph, overlap is an intrinsic property of the maximal-clique graph. Attributing to this property, the new representation scheme al-lows multiobjective evolutionary algorithms to handle the over-lapping community detection problem in a way similar to that of the separated community detection, such that the optimization problems are simplified. As a result, the proposed algorithm could detect overlapping community structure with higher partition accuracy and lower computational cost when compared with the existing ones. The experiments on both synthetic and real-world networks validate the effectiveness and efficiency of the proposed algorithm

Median evidential c-means algorithm and its application to community detection

Median clustering is of great value for partitioning relational data. In this paper, a new prototype-based clustering method, called Median Evidential C-Means (MECM), which is an extension of median c-means and median fuzzy c-means on the theoretical framework of belief functions is proposed. The median variant relaxes the restriction of a metric space embedding for the objects but constrains the prototypes to be in the original data set. Due to these properties, MECM could be applied to graph clustering problems. A community detection scheme for social networks based on MECM is investigated and the obtained credal partitions of graphs, which are more refined than crisp and fuzzy ones, enable us to have a better understanding of the graph structures. An initial prototype-selection scheme based on evidential semi-centrality is presented to avoid local premature convergence and an evidential modularity function is defined to choose the optimal number of communities. Finally, experiments in synthetic and real data sets illustrate the performance of MECM and show its difference to other methods

Combined node and link partitions method for finding overlapping communities in complex networks

Community detection in complex networks is a fundamental data analysis task in various domains, and how to effectively find overlapping communities in real applications is still a challenge. In this work, we propose a new unified model and method for finding the best overlapping communities on the basis of the associated node and link partitions derived from the same framework. Specifically, we first describe a unified model that accommodates node and link communities (partitions) together, and then present a nonnegative matrix factorization method to learn the parameters of the model. Thereafter, we infer the overlapping communities based on the derived node and link communities, i.e., determine each overlapped community between the corresponding node and link community with a greedy optimization of a local community function conductance. Finally, we introduce a model selection method based on consensus clustering to determine the number of communities. We have evaluated our method on both synthetic and real-world networks with ground-truths, and compared it with seven state-of-the-art methods. The experimental results demonstrate the superior performance of our method over the competing ones in detecting overlapping communities for all analysed data sets. Improved performance is particularly pronounced in cases of more complicated networked community structures

Communicability Graph and Community Structures in Complex Networks

We use the concept of the network communicability (Phys. Rev. E 77 (2008) 036111) to define communities in a complex network. The communities are defined as the cliques of a communicability graph, which has the same set of nodes as the complex network and links determined by the communicability function. Then, the problem of finding the network communities is transformed to an all-clique problem of the communicability graph. We discuss the efficiency of this algorithm of community detection. In addition, we extend here the concept of the communicability to account for the strength of the interactions between the nodes by using the concept of inverse temperature of the network. Finally, we develop an algorithm to manage the different degrees of overlapping between the communities in a complex network. We then analyze the USA airport network, for which we successfully detect two big communities of the eastern airports and of the western/central airports as well as two bridging central communities. In striking contrast, a well-known algorithm groups all but two of the continental airports into one community.Comment: 36 pages, 5 figures, to appear in Applied Mathematics and Computatio

Finding overlapping communities based on Markov chain and link clustering

Since community structure is an important feature of complex network, the study of community detection has attracted more and more attention in recent years. Despite most researchers focus on identifying disjoint communities, communities in many real networks often overlap. In this paper, we proposed a novel MCLC algorithm to discover overlapping communities, which using random walk on the line graph and attraction intensity. Unlike traditional random walk starting from a node, our random walk starts from a link. First we transform an undirected network graph to a weighted line graph, and then random walks on this line graph can be associated with a Markov chain. By calculating the transition probability of the Markov chain, we obtain the similarity between link pairs. Next the links can be clustered into “link communities” by a linkage method, and these nodes between link communities can be overlapping nodes. When converting the “link communities” into the “node communities”, we make a definition of attraction intensity to control the overlapping size. Finally the detected communities are permitted overlapped. Experiments on synthetic networks and some real world networks validate the effectiveness and efficiency of the proposed algorithm. Comparing overlapping modularity Qov with other related algorithms, the results of this algorithm are satisfactory