In many applications, it is common practice to obtain a network from interaction counts by thresholding each pairwise count at a prescribed value. Our analysis calls attention to the dependence of certain methods, notably Newman–Girvan modularity, on the choice of threshold. Essentially, the threshold either separates the network into clusters automatically, making the algorithm’s job trivial, ...

An epidemic is malicious code running on a subset of a community, a homogeneous set of instances of an application. Syzygy is an epidemic detection framework that looks for time-correlated anomalies, i.e., divergence from a model of dynamic behavior. We show mathematically and experimentally that, by leveraging the statistical properties of a large community, Syzygy is able to detect epidemics ...

Detecting community structure is fundamental for uncovering the links between structure and function in complex networks and for practical applications in many disciplines such as biology and sociology. A popular method now widely used relies on the optimization of a quantity called modularity, which is a quality index for a partition of a network into communities. We find that modularity optim...

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 repeatedl...

Many methods have been proposed for community detection in networks. Some of the most promising are methods based on statistical inference, which rest on solid mathematical foundations and return excellent results in practice. In this paper we show that two of the most widely used inference methods can be mapped directly onto versions of the standard minimum-cut graph partitioning problem, whic...

We propose a quantitative function for community partition -- i.e., modularity density or D value. We demonstrate that this quantitative function is superior to the widely used modularity Q and also prove its equivalence with the objective function of the kernel k means. Both theoretical and numerical results show that optimizing the new criterion not only can resolve detailed modules that exis...

Community structure represents the local organization of complex networks and the single most important feature to extract functional relationships between nodes. In the last years, the problem of community detection has been reformulated in terms of the optimization of a function, the Newman-Girvan modularity, that is supposed to express the quality of the partitions of a network into communit...

Starting from a general ansatz, we show how community detection can be interpreted as finding the ground state of an infinite range spin glass. Our approach applies to weighted and directed networks alike. It contains the ad hoc introduced quality function from [J. Reichardt and S. Bornholdt, Phys. Rev. Lett. 93, 218701 (2004)] and the modularity Q as defined by Newman and Girvan [Phys. Rev. E ...

Each day, millions of people ask questions and search for answers on the World Wide Web. Due to this, the Internet has grown to a world wide database of questions and answers, accessible to almost everyone. Since this database is so huge, it is hard to find out whether a question has been answered or even asked before. As a consequence, users are asking the same questions again and again, produ...

Network community detection—the problem of dividing a network of interest into clusters for intelligent analysis—has recently attracted significant attention in diverse fields of research. To discover intrinsic community structure a quantitative measure called modularity has been widely adopted as an optimization objective. Unfortunately, modularity is inherently NP-hard to optimize and approxi...