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Register a new userA General Definition of Network Communities and the Corresponding Detection Algorithm
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Network structures, consisting of nodes and edges, have applications in almost all subjects. A set of nodes is called a community if the nodes have strong interrelations. Industries (including cell phone carriers and online social media companies) need community structures to allocate network resources and provide proper and accurate services. However, all the current detection algorithms are motivated by the practical problems, whose applicabilities in other fields are open to question. Thence, for a new community problem, researchers need to derive algorithms ad hoc, which is arduous and even unnecessary. In this paper, we represent a general procedure to find community structures in practice. We mainly focus on two typical types of networks: transmission networks and similarity networks. We reduce them to a unified graph model, based on which we propose a general method to define and detect communities. Readers can specialize our general algorithm to accommodate their problems. In the end, we also give a demonstration to show how the algorithm works.
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Detecting communities in large-scale networks is a challenging task when each vertex may belong to multiple communities, as is often the case in social networks. The multiple memberships of vertices and thus the strong overlaps among communities render many detection algorithms invalid. We develop a Partial Community Merger Algorithm (PCMA) for detecting communities with significant overlaps as well as slightly overlapping and disjoint ones. It is a bottom-up approach based on properly reassembling partial information of communities revealed in ego networks of vertices to reconstruct complete communities. Noise control and merger order are the two key issues in implementing this idea. We propose a novel similarity measure between two merged communities that can suppress noise and an efficient algorithm that recursively merges the most similar pair of communities. The validity and accuracy of PCMA is tested against two benchmarks and compared to four existing algorithms. It is the most efficient one with linear complexity and it outperforms the compared algorithms when vertices have multiple memberships. PCMA is applied to two huge online social networks, Friendster and Sina Weibo. Millions of communities are detected and they are of higher qualities than the corresponding metadata groups. We find that the latter should not be regarded as the ground-truth of structural communities. The significant overlapping pattern found in the detected communities confirms the need of new algorithms, such as PCMA, to handle multiple memberships of vertices in social networks.
In network science, assortativity refers to the tendency of links to exist between nodes with similar attributes. In social networks, for example, links tend to exist between individuals of similar age, nationality, location, race, income, educational level, religious belief, and language. Thus, various attributes jointly affect the network topology. An interesting problem is to detect community structure beyond some specific assortativity-related attributes $rho$, i.e., to take out the effect of $rho$ on network topology and reveal the hidden community structure which are due to other attributes. An approach to this problem is to redefine the null model of the modularity measure, so as to simulate the effect of $rho$ on network topology. However, a challenge is that we do not know to what extent the network topology is affected by $rho$ and by other attributes. In this paper, we propose Dist-Modularity which allows us to freely choose any suitable function to simulate the effect of $rho$. Such freedom can help us probe the effect of $rho$ and detect the hidden communities which are due to other attributes. We test the effectiveness of Dist-Modularity on synthetic benchmarks and two real-world networks.
In this paper, a new comparative definition for community in networks is proposed and the corresponding detecting algorithm is given. A community is defined as a set of nodes, which satisfy that each nodes degree inside the community should not be smaller than the nodes degree toward any other community. In the algorithm, the attractive force of a community to a node is defined as the connections between them. Then employing attractive force based self-organizing process, without any extra parameter, the best communities can be detected. Several artificial and real-world networks, including Zachary Karate club network and College football network are analyzed. The algorithm works well in detecting communities and it also gives a nice description for network division and group formation.
With invaluable theoretical and practical benefits, the problem of partitioning networks for community structures has attracted significant research attention in scientific and engineering disciplines. In literature, Newmans modularity measure is routinely applied to quantify the quality of a given partition, and thereby maximizing the measure provides a principled way of detecting communities in networks. Unfortunately, the exact optimization of the measure is computationally NP-complete and only applicable to very small networks. Approximation approaches have to be sought to scale to large networks. To address the computational issue, we proposed a new method to identify the partition decisions. Coupled with an iterative rounding strategy and a fast constrained power method, our work achieves tight and effective spectral relaxations. The proposed method was evaluated thoroughly on both real and synthetic networks. Compared with state-of-the-art approaches, the method obtained comparable, if not better, qualities. Meanwhile, it is highly suitable for parallel execution and reported a nearly linear improvement in running speed when increasing the number of computing nodes, which thereby provides a practical tool for partitioning very large networks.
We study the structure of loops in networks using the notion of modulus of loop families. We introduce a new measure of network clustering by quantifying the richness of families of (simple) loops. Modulus tries to minimize the expected overlap among loops by spreading the expected link-usage optimally. We propose weighting networks using these expected link-usages to improve classical community detection algorithms. We show that the proposed method enhances the performance of certain algorithms, such as spectral partitioning and modularity maximization heuristics, on standard benchmarks.
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