Related papers: The Hierarchy of Block Models

A generalization of modularity, called block modularity, is defined. This is a quality function which evaluates a label assignment against an arbitrary block pattern. Therefore, unlike standard modularity or its variants, arbitrary network…

A myriad of approaches have been proposed to characterise the mesoscale structure of networks - most often as a partition based on patterns variously called communities, blocks, or clusters. Clearly, distinct methods designed to detect…

In Stochastic blockmodels, which are among the most prominent statistical models for cluster analysis of complex networks, clusters are defined as groups of nodes with statistically similar link probabilities within and between groups. A…

The bipartite network appears in various areas, such as biology, sociology, physiology, and computer science. \cite{rohe2016co} proposed Stochastic co-Blockmodel (ScBM) as a tool for detecting community structure of binary bipartite graph…

A long-standing open problem with direct blockmodeling is that it is explicitly intended for binary, not valued, networks. The underlying dilemma is how empirical valued blocks can be compared with ideal binary blocks, an intrinsic problem…

The paper presents several approaches to generalized blockmodeling of valued networks, where values of the ties are assumed to be measured on at least interval scale. The first approach is a straightforward generalization of the generalized…

We propose a model to address the overlooked problem of node clustering in simple hypergraphs. Simple hypergraphs are suitable when a node may not appear multiple times in the same hyperedge, such as in co-authorship datasets. Our model…

The article presents several approaches to the blockmodeling of multilevel network data. Multilevel network data consist of networks that are measured on at least two levels (e.g. between organizations and people) and information on ties…

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…

Many real world networks consist of multiple types of nodes with edges that are heterogeneous in nature. However, most of the existing work for community detection only focused on homogeneous network consisting of a single layer. In this…

In urban spatial networks, there is an interdependency between neighborhood roles and the transportation methods between neighborhoods. In this paper, we classify docking stations in bicycle-sharing networks to gain insight into the human…

Spectral embedding of network adjacency matrices often produces node representations living approximately around low-dimensional submanifold structures. In particular, hidden substructure is expected to arise when the graph is generated…

We present a Bayesian formulation of weighted stochastic block models that can be used to infer the large-scale modular structure of weighted networks, including their hierarchical organization. Our method is nonparametric, and thus does…

Community detection approaches resolve complex networks into smaller groups (communities) that are expected to be relatively edge-dense and well-connected. The stochastic block model (SBM) is one of several approaches used to uncover…

Clustering the nodes of a graph allows the analysis of the topology of a network. The stochastic block model is a clustering method based on a probabilistic model. Initially developed for binary networks it has recently been extended to…

We consider community detection in Degree-Corrected Stochastic Block Models (DC-SBM). We propose a spectral clustering algorithm based on a suitably normalized adjacency matrix. We show that this algorithm consistently recovers the…

Labelled networks are an important class of data, naturally appearing in numerous applications in science and engineering. A typical inference goal is to determine how the vertex labels (or features) affect the network's structure. In this…

In this short note, we address the identifiability issues inherent in the Degree-Corrected Stochastic Block Model (DCSBM). We provide a rigorous proof demonstrating that the parameters of the DCSBM are identifiable up to a scaling factor…

Probabilistic graphic model is an elegant framework to compactly present complex real-world observations by modeling uncertainty and logical flow (conditionally independent factors). In this paper, we present a probabilistic framework of…

Discovering and characterizing the large-scale topological features in empirical networks are crucial steps in understanding how complex systems function. However, most existing methods used to obtain the modular structure of networks…