Related papers: Universality of the stochastic block model
Multi-layer networks arise naturally in various domains including biology, finance and sociology, among others. The multi-layer stochastic block model (multi-layer SBM) is commonly used for community detection in the multi-layer networks.…
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…
Semidefinite programming is an important tool to tackle several problems in data science and signal processing, including clustering and community detection. However, semidefinite programs are often slow in practice, so speed up techniques…
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…
We discuss two views on extending existing methods for complex network modeling which we dub the communities first and the networks first view, respectively. Inspired by the networks first view that we attribute to White, Boorman, and…
A common method for delineating urban and suburban boundaries is to identify clusters of spatial units that are highly interconnected in a network of commuting flows, each cluster signaling a cohesive economic submarket. It is critical that…
This paper proposes a novel scalable community-based neural framework for graph learning. The framework learns the graph topology through the task of community detection and link prediction by optimizing with our proposed joint SBM loss…
The mixed membership stochastic blockmodel (MMSB) is a popular Bayesian network model for community detection. Fitting such large Bayesian network models quickly becomes computationally infeasible when the number of nodes grows into…
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…
The stochastic block model (SBM) is a probabilistic model de- signed to describe heterogeneous directed and undirected graphs. In this paper, we address the asymptotic inference on SBM by use of maximum- likelihood and variational…
The problem of detecting communities in a graph is maybe one the most studied inference problems, given its simplicity and widespread diffusion among several disciplines. A very common benchmark for this problem is the stochastic block…
The Boltzmann Machine (BM) is a neural network composed of stochastically firing neurons that can learn complex probability distributions by adapting the synaptic interactions between the neurons. BMs represent a very generic class of…
We present a Markov chain Monte Carlo scheme based on merges and splits of groups that is capable of efficiently sampling from the posterior distribution of network partitions, defined according to the stochastic block model (SBM). We…
A key topic in network science is the detection of intermediate or meso-scale structures. Community, core-periphery, disassortative and other partitions allow us to understand the organisation and function of large networks. In this work we…
Stochastic Block Models (SBMs) are a fundamental tool for community detection in network analysis. But little theoretical work exists on the statistical performance of Bayesian SBMs, especially when the community count is unknown. This…
The stochastic block model (SBM) with two communities, or equivalently the planted bisection model, is a popular model of random graph exhibiting a cluster behaviour. In the symmetric case, the graph has two equally sized clusters and…
Motivated by the prevalent data science applications of processing large-scale graph data such as social networks and biological networks, this paper investigates lossless compression of data in the form of a labeled graph. Particularly, we…
The community detection problem requires to cluster the nodes of a network into a small number of well-connected "communities". There has been substantial recent progress in characterizing the fundamental statistical limits of community…
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…
The stochastic block model is one of the oldest and most ubiquitous models for studying clustering and community detection. In an exciting sequence of developments, motivated by deep but non-rigorous ideas from statistical physics, Decelle…