Detectability thresholds and optimal algorithms for community structure in dynamic networks

We consider an approach for community detection in time-varying networks. At its core, this approach maintains a small sketch graph to capture the essential community structure found in each snapshot of the full network. We demonstrate how the sketch can be used to explicitly identify six key community events which typically occur during network evolution: growth, shrinkage, merging, splitting, birth and death. Based on these detection techniques, we formulate a community det...

This paper studies change point detection on networks with community structures. It proposes a framework that can detect both local and global changes in networks efficiently. Importantly, it can clearly distinguish the two types of changes. The framework design is generic and as such several state-of-the-art change point detection algorithms can fit in this design. Experiments on both synthetic and real-world networks show that this framework can accurately detect changes wh...

We study bipartite community detection in networks, or more generally the network biclustering problem. We present a fast two-stage procedure based on spectral initialization followed by the application of a pseudo-likelihood classifier twice. Under mild regularity conditions, we establish the weak consistency of the procedure (i.e., the convergence of the misclassification rate to zero) under a general bipartite stochastic block model. We show that the procedure is optimal i...

Community structure in networks has been investigated from many viewpoints, usually with the same end result: a community detection algorithm of some kind. Recent research offers methods for combining the results of such algorithms into timelines of community evolution. This paper investigates community detection and tracking from the data fusion perspective. We avoid the kind of hard calls made by traditional community detection algorithms in favor of retaining as much uncer...

Community discovery is one of the most studied problems in network science. In recent years, many works have focused on discovering communities in temporal networks, thus identifying dynamic communities. Interestingly, dynamic communities are not mere sequences of static ones; new challenges arise from their dynamic nature. In this chapter, we will discuss some of these challenges and recent propositions to tackle them. We will, among other topics, discuss on the question of ...

An adaptive label propagation algorithm (ALPA) is proposed to detect and monitor communities in dynamic networks. Unlike the traditional methods by re-computing the whole community decomposition after each modification of the network, ALPA takes into account the information of historical communities and updates its solution according to the network modifications via a local label propagation process, which generally affects only a small portion of the network. This makes it r...

Statistical node clustering in discrete time dynamic networks is an emerging field that raises many challenges. Here, we explore statistical properties and frequentist inference in a model that combines a stochastic block model (SBM) for its static part with independent Markov chains for the evolution of the nodes groups through time. We model binary data as well as weighted dynamic random graphs (with discrete or continuous edges values). Our approach, motivated by the impor...

We propose a first-order autoregressive (i.e. AR(1)) model for dynamic network processes in which edges change over time while nodes remain unchanged. The model depicts the dynamic changes explicitly. It also facilitates simple and efficient statistical inference methods including a permutation test for diagnostic checking for the fitted network models. The proposed model can be applied to the network processes with various underlying structures but with independent edges. As...

A common goal in network modeling is to uncover the latent community structure present among nodes. For many real-world networks, the true connections consist of events arriving as streams, which are then aggregated to form edges, ignoring the dynamic temporal component. A natural way to take account of these temporal dynamics of interactions is to use point processes as the foundation of network models for community detection. Computational complexity hampers the scalability...

Significant efforts have gone into the development of statistical models for analyzing data in the form of networks, such as social networks. Most existing work has focused on modeling static networks, which represent either a single time snapshot or an aggregate view over time. There has been recent interest in statistical modeling of dynamic networks, which are observed at multiple points in time and offer a richer representation of many complex phenomena. In this paper, we...