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We derive rigorous bounds for well-defined community structure in complex networks for a stochastic block model (SBM) benchmark. In particular, we analyze the effect of inter-community "noise" (inter-community edges) on any "community…

This paper deals with non-observed dyads during the sampling of a network and consecutive issues in the inference of the Stochastic Block Model (SBM). We review sampling designs and recover Missing At Random (MAR) and Not Missing At Random…

Networks are a commonly used mathematical model to describe the rich set of interactions between objects of interest. Many clustering methods have been developed in order to partition such structures, among which several rely on underlying…

Identifying the number of communities is a fundamental problem in community detection, which has received increasing attention recently. However, rapid advances in technology have led to the emergence of large-scale networks in various…

Signed network structure discovery has received extensive attention and has become a research focus in the field of network science. However, most of the existing studies are focused on the networks with a single structure, e.g., community…

We introduce the Markov Stochastic Block Model (MSBM): a growth model for community based networks where node attributes are assigned through a Markovian dynamic. We rely on HMMs' literature to design prediction methods that are robust to…

Community detection, discovering the underlying communities within a network from observed connections, is a fundamental problem in network analysis, yet it remains underexplored for signed networks. In signed networks, both edge connection…

Modeling structure in complex networks using Bayesian non-parametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This paper provides a gentle introduction to…

Stochastic blockmodels have been proposed as a tool for detecting community structure in networks as well as for generating synthetic networks for use as benchmarks. Most blockmodels, however, ignore variation in vertex degree, making them…

Higher-order motif structures and multi-vertex interactions are becoming increasingly important in studies that aim to improve our understanding of functionalities and evolution patterns of networks. To elucidate the role of higher-order…

Hierarchical Bayesian networks and neural networks with stochastic hidden units are commonly perceived as two separate types of models. We show that either of these types of models can often be transformed into an instance of the other, by…

Networks are useful representations of many systems with interacting entities, such as social, biological and physical systems. Characterizing the meso-scale organization, i.e. the community structure, is an important problem in network…

Real-world networks usually have community structure, that is, nodes are grouped into densely connected communities. Community detection is one of the most popular and best-studied research topics in network science and has attracted…

Community detection for large networks poses challenges due to the high computational cost as well as heterogeneous community structures. In this paper, we consider widely existing real-world networks with ``grouped communities'' (or ``the…

Stochastic Block Models (SBMs) are a popular approach to modeling single real-world graphs. The key idea of SBMs is to partition the vertices of the graph into blocks with similar edge densities within, as well as between different blocks.…

Networks, which represent agents and interactions between them, arise in myriad applications throughout the sciences, engineering, and even the humanities. To understand large-scale structure in a network, a common task is to cluster a…

Many kinds of data can be represented as a network or graph. It is crucial to infer the latent structure underlying such a network and to predict unobserved links in the network. Mixed Membership Stochastic Blockmodel (MMSB) is a promising…

The stochastic block model (SBM) is a widely used framework for community detection in networks, where the network structure is typically represented by an adjacency matrix. However, conventional SBMs are not directly applicable to an…

In the model-based clustering of networks, blockmodelling may be used to identify roles in the network. We identify a special case of the Stochastic Block Model (SBM) where we constrain the cluster-cluster interactions such that the density…

Bayesian inference allows us to define a posterior distribution over the weights of a generic neural network (NN). Exact posteriors are usually intractable, in which case approximations can be employed. One such approximation - variational…