Related papers: Bootstrap percolation on the stochastic block mode…
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…
We propose a robust, scalable, integrated methodology for community detection and community comparison in graphs. In our procedure, we first embed a graph into an appropriate Euclidean space to obtain a low-dimensional representation, and…
Bootstrap percolation provides an emblematic instance of phase behavior characterised by an abrupt transition with diverging critical fluctuations. This unusual hybrid situation generally occurs in particle systems in which the occupation…
We study bootstrap percolation (BP) on hyperbolic lattices obtained by regular tilings of the hyperbolic plane. Our work is motivated by the connection between the BP transition and the dynamical transition of kinetically constrained…
Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component. Despite its very simple rules, percolation theory has successfully been applied…
We introduce the simplest model which relates the emergence of collective social/economic phenomena to the existence of a (possibly self-organized) percolation transition. We suggest a series of extensions to financial, economic, political…
In complex network research clique percolation, introduced by Palla et al., is a deterministic community detection method, which allows for overlapping communities and is purely based on local topological properties of a network. Here we…
We present an exact mathematical framework able to describe site-percolation transitions in real multiplex networks. Specifically, we consider the average percolation diagram valid over an infinite number of random configurations where…
Network homophily, the tendency of similar nodes to be connected, and transitivity, the tendency of two nodes being connected if they share a common neighbor, are conflated properties in network analysis, since one mechanism can drive the…
We study atypical behavior in bootstrap percolation on the Erd\H{o}s-R\'enyi random graph. Initially a set $S$ is infected. Other vertices are infected once at least $r$ of their neighbors become infected. Janson et al. (2012) locates the…
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…
We consider the spectral properties of balanced stochastic block models of which the average degree grows slower than the number of nodes (sparse regime) or proportional to it (dense regime). For both regimes, we prove a phase transition of…
The notion of k-clique percolation in random graphs is introduced, where k is the size of the complete subgraphs whose large scale organizations are analytically and numerically investigated. For the Erdos-Renyi graph of N vertices we…
Multilayer networks are a useful data structure for simultaneously capturing multiple types of relationships between a set of nodes. In such networks, each relational definition gives rise to a layer. While each layer provides its own set…
We study the hierarchy of communities in real-world networks under a generic stochastic block model, in which the connection probabilities are structured in a binary tree. Under such model, a standard recursive bi-partitioning algorithm is…
We examine bootstrap percolation in d-dimensional, directed metric graphs in the context of recent measurements of firing dynamics in 2D neuronal cultures. There are two regimes, depending on the graph size N. Large metric graphs are…
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…
We construct a novel class of stochastic blockmodels using Bayesian nonparametric mixtures. These model allows us to jointly estimate the structure of multiple networks and explicitly compare the community structures underlying them, while…
Classical blockmodel is known as the simplest among models of networks with community structure. The model can be also seen as an extremely simply example of interconnected networks. For this reason, it is surprising that the percolation…
An efficient MCMC algorithm is presented to cluster the nodes of a network such that nodes with similar role in the network are clustered together. This is known as block-modelling or block-clustering. The model is the stochastic blockmodel…