Fast Multi-Scale Community Detection based on Local Criteria within a Multi-Threaded Algorithm

Many systems can be described using graphs, or networks. Detecting communities in these networks can provide information about the underlying structure and functioning of the original systems. Yet this detection is a complex task and a large amount of work was dedicated to it in the past decade. One important feature is that communities can be found at several scales, or levels of resolution, indicating several levels of organisations. Therefore solutions to the community structure may not be unique. Also networks tend to be large and hence require efficient processing. In this work, we present a new algorithm for the fast detection of communities across scales using a local criterion. We exploit the local aspect of the criterion to enable parallel computation and improve the algorithm's efficiency further. The algorithm is tested against large generated multi-scale networks and experiments demonstrate its efficiency and accuracy.Comment: arXiv admin note: text overlap with arXiv:1204.100

Detecting highly overlapping community structure by greedy clique expansion

In complex networks it is common for each node to belong to several communities, implying a highly overlapping community structure. Recent advances in benchmarking indicate that existing community assignment algorithms that are capable of detecting overlapping communities perform well only when the extent of community overlap is kept to modest levels. To overcome this limitation, we introduce a new community assignment algorithm called Greedy Clique Expansion (GCE). The algorithm identifies distinct cliques as seeds and expands these seeds by greedily optimizing a local fitness function. We perform extensive benchmarks on synthetic data to demonstrate that GCE's good performance is robust across diverse graph topologies. Significantly, GCE is the only algorithm to perform well on these synthetic graphs, in which every node belongs to multiple communities. Furthermore, when put to the task of identifying functional modules in protein interaction data, and college dorm assignments in Facebook friendship data, we find that GCE performs competitively.Comment: 10 pages, 7 Figures. Implementation source and binaries available at http://sites.google.com/site/greedycliqueexpansion

Correlation-Based Community Detection

Mining community structures from the complex network is an important problem across a variety of fields. Many existing community detection methods detect communities through optimizing a community evaluation function. However, most of these functions even have high values on random graphs and may fail to detect small communities in the large-scale network (the so-called resolution limit problem). In this paper, we introduce two novel node-centric community evaluation functions by connecting correlation analysis with community detection. We will further show that the correlation analysis can provide a novel theoretical framework which unifies some existing evaluation functions in the context of a correlation-based optimization problem. In this framework, we can mitigate the resolution limit problem and eliminate the influence of random fluctuations by selecting the right correlation function. Furthermore, we introduce three key properties used in mining association rule into the context of community detection to help us choose the appropriate correlation function. Based on our introduced correlation functions, we propose a community detection algorithm called CBCD. Our proposed algorithm outperforms existing state-of-the-art algorithms on both synthetic benchmark networks and real-world networks

Ensemble-Based Discovery of Disjoint, Overlapping and Fuzzy Community Structures in Networks

Though much work has been done on ensemble clustering in data mining, the application of ensemble methods to community detection in networks is in its infancy. In this paper, we propose two ensemble methods: ENDISCO and MEDOC. ENDISCO performs disjoint community detection. In contrast, MEDOC performs disjoint, overlapping, and fuzzy community detection and represents the first ever ensemble method for fuzzy and overlapping community detection. We run extensive experiments with both algorithms against both synthetic and several real-world datasets for which community structures are known. We show that ENDISCO and MEDOC both beat the best-known existing standalone community detection algorithms (though we emphasize that they leverage them). In the case of disjoint community detection, we show that both ENDISCO and MEDOC beat an existing ensemble community detection algorithm both in terms of multiple accuracy measures and run-time. We further show that our ensemble algorithms can help explore core-periphery structure of network communities, identify stable communities in dynamic networks and help solve the "degeneracy of solutions" problem, generating robust results

Efficiently Detecting Overlapping Communities through Seeding and Semi-Supervised Learning

Seeding then expanding is a commonly used scheme to discover overlapping communities in a network. Most seeding methods are either too complex to scale to large networks or too simple to select high-quality seeds, and the non-principled functions used by most expanding methods lead to poor performance when applied to diverse networks. This paper proposes a new method that transforms a network into a corpus where each edge is treated as a document, and all nodes of the network are treated as terms of the corpus. An effective seeding method is also proposed that selects seeds as a training set, then a principled expanding method based on semi-supervised learning is applied to classify edges. We compare our new algorithm with four other community detection algorithms on a wide range of synthetic and empirical networks. Experimental results show that the new algorithm can significantly improve clustering performance in most cases. Furthermore, the time complexity of the new algorithm is linear to the number of edges, and this low complexity makes the new algorithm scalable to large networks

Real-Time Community Detection in Large Social Networks on a Laptop

For a broad range of research, governmental and commercial applications it is important to understand the allegiances, communities and structure of key players in society. One promising direction towards extracting this information is to exploit the rich relational data in digital social networks (the social graph). As social media data sets are very large, most approaches make use of distributed computing systems for this purpose. Distributing graph processing requires solving many difficult engineering problems, which has lead some researchers to look at single-machine solutions that are faster and easier to maintain. In this article, we present a single-machine real-time system for large-scale graph processing that allows analysts to interactively explore graph structures. The key idea is that the aggregate actions of large numbers of users can be compressed into a data structure that encapsulates user similarities while being robust to noise and queryable in real-time. We achieve single machine real-time performance by compressing the neighbourhood of each vertex using minhash signatures and facilitate rapid queries through Locality Sensitive Hashing. These techniques reduce query times from hours using industrial desktop machines operating on the full graph to milliseconds on standard laptops. Our method allows exploration of strongly associated regions (i.e. communities) of large graphs in real-time on a laptop. It has been deployed in software that is actively used by social network analysts and offers another channel for media owners to monetise their data, helping them to continue to provide free services that are valued by billions of people globally

Local Partition in Rich Graphs

Local graph partitioning is a key graph mining tool that allows researchers to identify small groups of interrelated nodes (e.g. people) and their connective edges (e.g. interactions). Because local graph partitioning is primarily focused on the network structure of the graph (vertices and edges), it often fails to consider the additional information contained in the attributes. In this paper we propose---(i) a scalable algorithm to improve local graph partitioning by taking into account both the network structure of the graph and the attribute data and (ii) an application of the proposed local graph partitioning algorithm (AttriPart) to predict the evolution of local communities (LocalForecasting). Experimental results show that our proposed AttriPart algorithm finds up to 1.6$\times$ denser local partitions, while running approximately 43$\times$ faster than traditional local partitioning techniques (PageRank-Nibble). In addition, our LocalForecasting algorithm shows a significant improvement in the number of nodes and edges correctly predicted over baseline methods.Comment: Under KDD 2018 revie

GenPerm: A Unified Method for Detecting Non-overlapping and Overlapping Communities

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.Comment: This paper (final version) is accepted in IEEE Transactions on Knowledge and Data Engineering (TKDE). 13 Figures, 6 table

Identification of Overlapping Communities by Locally Calculating Community-Changing Resolution Levels

An algorithm for the detection of overlapping natural communities in networks was proposed by Lancichinetti, Fortunato, and Kertesz (LFK) last year. The LFK algorithm constructs natural communities of (in principle) all nodes of a graph by maximising the local fitness of communities. The resulting modules can overlap. The generation of communities can easily be repeated for many values of resolution; thus allowing different views on the network at different resolutions. We implemented the main idea of the LFK algorithm---to generate natural communities of each node of a network---in a different way. We start with a value of the resolution parameter that is high enough for each node to be its own natural community. As soon as the resolution is reduced, each node acquires other nodes as members of its community, i.e. natural communities grow. For each community found at a certain resolution level we calculate the next lower resolution where a node is added. After adding a node to a community of a seed node we check whether it is also the natural community of a node that we have already analysed. In this case, we can stop expanding the seed node's community. We tested our algorithm on a small benchmark graph and on a network of about 500 papers in information science (weighted with the Salton index of bibliographic coupling). In our tests, this approach results in characteristic ranges of resolution where a large resolution change does not lead to a growth of the natural community. Such stable modules were also obtained by applying the LFK algorithm but since we determine communities for all resolution values in one run, our approach is faster than the LFK reference. And our algorithm reveals the hierarchical structure of the graph more easily.Comment: 10 pages, 12 figures, also presented as "A local algorithm to get overlapping communities at all resolution levels in one run" in a poster session at ASONAM conference, Odense, Denmark, August 201

A Survey of Community Search Over Big Graphs

With the rapid development of information technologies, various big graphs are prevalent in many real applications (e.g., social media and knowledge bases). An important component of these graphs is the network community. Essentially, a community is a group of vertices which are densely connected internally. Community retrieval can be used in many real applications, such as event organization, friend recommendation, and so on. Consequently, how to efficiently find high-quality communities from big graphs is an important research topic in the era of big data. Recently a large group of research works, called community search, have been proposed. They aim to provide efficient solutions for searching high-quality communities from large networks in real-time. Nevertheless, these works focus on different types of graphs and formulate communities in different manners, and thus it is desirable to have a comprehensive review of these works. In this survey, we conduct a thorough review of existing community search works. Moreover, we analyze and compare the quality of communities under their models, and the performance of different solutions. Furthermore, we point out new research directions. This survey does not only help researchers to have a better understanding of existing community search solutions, but also provides practitioners a better judgment on choosing the proper solutions