Different approaches to community detection

A precise definition of what constitutes a community in networks has remained elusive. Consequently, network scientists have compared community detection algorithms on benchmark networks with a particular form of community structure and classified them based on the mathematical techniques they employ. However, this comparison can be misleading because apparent similarities in their mathematical machinery can disguise different reasons for why we would want to employ community detection in the first place. Here we provide a focused review of these different motivations that underpin community detection. This problem-driven classification is useful in applied network science, where it is important to select an appropriate algorithm for the given purpose. Moreover, highlighting the different approaches to community detection also delineates the many lines of research and points out open directions and avenues for future research.Comment: 14 pages, 2 figures. Written as a chapter for forthcoming Advances in network clustering and blockmodeling, and based on an extended version of The many facets of community detection in complex networks, Appl. Netw. Sci. 2: 4 (2017) by the same author

Community detection in network analysis: a survey

The existence of community structures in networks is not unusual, including in the domains of sociology, biology, and business, etc. The characteristic of the community structure is that nodes of the same community are highly similar while on the contrary, nodes across communities present low similarity. In academia, there is a surge in research efforts on community detection in network analysis, especially in developing statistically sound methodologies for exploring, modeling, and interpreting these kind of structures and relationships. This survey paper aims to provide a brief review of current applicable statistical methodologies and approaches in a comparative manner along with metrics for evaluating graph clustering results and application using R. At the end, we provide promising future research directions.Statistic

Evaluating Overfit and Underfit in Models of Network Community Structure

A common data mining task on networks is community detection, which seeks an unsupervised decomposition of a network into structural groups based on statistical regularities in the network's connectivity. Although many methods exist, the No Free Lunch theorem for community detection implies that each makes some kind of tradeoff, and no algorithm can be optimal on all inputs. Thus, different algorithms will over or underfit on different inputs, finding more, fewer, or just different communities than is optimal, and evaluation methods that use a metadata partition as a ground truth will produce misleading conclusions about general accuracy. Here, we present a broad evaluation of over and underfitting in community detection, comparing the behavior of 16 state-of-the-art community detection algorithms on a novel and structurally diverse corpus of 406 real-world networks. We find that (i) algorithms vary widely both in the number of communities they find and in their corresponding composition, given the same input, (ii) algorithms can be clustered into distinct high-level groups based on similarities of their outputs on real-world networks, and (iii) these differences induce wide variation in accuracy on link prediction and link description tasks. We introduce a new diagnostic for evaluating overfitting and underfitting in practice, and use it to roughly divide community detection methods into general and specialized learning algorithms. Across methods and inputs, Bayesian techniques based on the stochastic block model and a minimum description length approach to regularization represent the best general learning approach, but can be outperformed under specific circumstances. These results introduce both a theoretically principled approach to evaluate over and underfitting in models of network community structure and a realistic benchmark by which new methods may be evaluated and compared.Comment: 22 pages, 13 figures, 3 table

Community Detection on Evolving Graphs

Clustering is a fundamental step in many information-retrieval and data-mining applications. Detecting clusters in graphs is also a key tool for finding the community structure in social and behavioral networks. In many of these applications, the input graph evolves over time in a continual and decentralized manner, and, to maintain a good clustering, the clustering algorithm needs to repeatedly probe the graph. Furthermore, there are often limitations on the frequency of such probes, either imposed explicitly by the online platform (e.g., in the case of crawling proprietary social networks like twitter) or implicitly because of resource limitations (e.g., in the case of crawling the web). In this paper, we study a model of clustering on evolving graphs that captures this aspect of the problem. Our model is based on the classical stochastic block model, which has been used to assess rigorously the quality of various static clustering methods. In our model, the algorithm is supposed to reconstruct the planted clustering, given the ability to query for small pieces of local information about the graph, at a limited rate. We design and analyze clustering algorithms that work in this model, and show asymptotically tight upper and lower bounds on their accuracy. Finally, we perform simulations, which demonstrate that our main asymptotic results hold true also in practice