Detectability thresholds and optimal algorithms for community structure in dynamic networks

We consider a time-ordered sequence of networks stemming from stochastic block models where nodes gradually change memberships over time and no network at any single time point contains sufficient signal strength to recover its community structure. To estimate the time-varying community structure, we develop KD-SoS (kernel debiased sum-of-square), a method performing spectral clustering after a debiased sum-of-squared aggregation of adjacency matrices. Our theory demonstrates...

Dynamic heterogeneous networks describe the temporal evolution of interactions among nodes and edges of different types. While there is a rich literature on finding communities in dynamic networks, the application of these methods to dynamic heterogeneous networks can be inappropriate, due to the involvement of different types of nodes and edges and the need to treat them differently. In this paper, we propose a statistical framework for detecting common communities in dynami...

Networks observed in real world like social networks, collaboration networks etc., exhibit temporal dynamics, i.e. nodes and edges appear and/or disappear over time. In this paper, we propose a generative, latent space based, statistical model for such networks (called dynamic networks). We consider the case where the number of nodes is fixed, but the presence of edges can vary over time. Our model allows the number of communities in the network to be different at different t...

Most real-world social networks are inherently dynamic, composed of communities that are constantly changing in membership. To track these evolving communities, we need dynamic community detection techniques. This article evaluates the performance of a set of game theoretic approaches for identifying communities in dynamic networks. Our method, D-GT (Dynamic Game Theoretic community detection), models each network node as a rational agent who periodically plays a community me...

This article studies the estimation of latent community memberships from pairwise interactions in a network of $N$ nodes, where the observed interactions can be of arbitrary type, including binary, categorical, and vector-valued, and not excluding even more general objects such as time series or spatial point patterns. As a generative model for such data, we introduce a stochastic block model with a general measurable interaction space $\mathcal S$, for which we derive inform...

Detecting community structures in social networks has gained considerable attention in recent years. However, lack of prior knowledge about the number of communities, and their overlapping nature have made community detection a challenging problem. Moreover, many of the existing methods only consider static networks, while most of real world networks are dynamic and evolve over time. Hence, finding consistent overlapping communities in dynamic networks without any prior knowl...

Although the computational and statistical trade-off for modeling single graphs, for instance, using block models is relatively well understood, extending such results to sequences of graphs has proven to be difficult. In this work, we take a step in this direction by proposing two models for graph sequences that capture: (a) link persistence between nodes across time, and (b) community persistence of each node across time. In the first model, we assume that the latent commun...

In principle, higher-order networks that have multiple edge types are more informative than their lower-order counterparts. In practice, however, excessively rich information may be algorithmically infeasible to extract. It requires an algorithm that assumes a high-dimensional model and such an algorithm may perform poorly or be extremely sensitive to the initial estimate of the model parameters. Herein, we address this problem of community detection through a detectability a...

The latent stochastic block model is a flexible and widely used statistical model for the analysis of network data. Extensions of this model to a dynamic context often fail to capture the persistence of edges in contiguous network snapshots. The recently introduced stochastic block transition model addresses precisely this issue, by modelling the probabilities of creating a new edge and of maintaining an edge over time. Using a model-based clustering approach, this paper illu...

We study community detection based on state observations from gossip opinion dynamics over stochastic block models (SBM). It is assumed that a network is generated from a two-community SBM where each agent has a community label and each edge exists with probability depending on its endpoints' labels. A gossip process then evolves over the sampled network. We propose two algorithms to detect the communities out of a single trajectory of the process. It is shown that, when the ...