相关论文: Bootstrap percolation on the stochastic block mode…

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…

We consider a directed version of the classical Stochastic Block Model with $m\ge 2$ communities and a parameter $\alpha$ controlling the inter-community connectivity. We show that, depending on the scaling of $\alpha$, the mixing time of…

Stochastic block models (SBMs) are a very commonly studied network model for community detection algorithms. In the standard form of an SBM, the $n$ vertices (or nodes) of a graph are generally divided into multiple pre-determined…

Community detection seeks to recover mesoscopic structure from network data that may be binary, count-valued, signed, directed, weighted, or multilayer. The stochastic block model (SBM) explains such structure by positing a latent partition…

This paper considers the problem of community detection on multiple potentially correlated graphs from an information-theoretical perspective. We first put forth a random graph model, called the multi-view stochastic block model (MVSBM),…

The `random intersection graph with communities' models networks with communities, assuming an underlying bipartite structure of groups and individuals. Each group has its own internal structure described by a (small) graph, while groups…

Bootstrap percolation is a simple but non-trivial model. It has applications in many areas of science and has been explored on random networks for several decades. In single layer (simplex) networks, it has been recently observed that…

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…

The diffusion and bootstrap percolation models were studied in regular random and Erd\H{o}s-R\'{e}nyi networks using the modified Newman-Ziff algorithms. We calculated the percolation threshold and the order parameter of the percolation…

Stochastic block models (SBMs) are often used to find assortative community structures in networks, such that the probability of connections within communities is higher than in between communities. However, classic SBMs are not limited to…

We make the first steps towards generalizing the theory of stochastic block models, in the sparse regime, towards a model where the discrete community structure is replaced by an underlying geometry. We consider a geometric random graph…

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…

Spectral clustering is a widely used method for community detection in networks. We focus on a semi-supervised community detection scenario in the Partially Labeled Stochastic Block Model (PL-SBM) with two balanced communities, where a…

Recent experimental studies of living neural networks reveal that their global activation induced by electrical stimulation can be explained using the concept of bootstrap percolation on a directed random network. The experiment consists in…

In this paper we extend our previous work on the stochastic block model, a commonly used generative model for social and biological networks, and the problem of inferring functional groups or communities from the topology of the network. We…

We consider a network, bonds of which are being sequentially removed; that is done at random, but conditioned on the system remaining connected (Self-Repairing Bond Percolation SRBP). This model is the simplest representative of a class of…

Majority bootstrap percolation is a monotone cellular automata that can be thought of as a model of infection spreading in networks. Starting with an initially infected set, new vertices become infected once more than half of their…

Bootstrap percolation in (random) graphs is a contagion dynamics among a set of vertices with certain threshold levels. The process is started by a set of initially infected vertices, and an initially uninfected vertex with threshold $k$…

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…

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…