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Communities are a common and widely studied structure in networks, typically under the assumption that the network is fully and correctly observed. In practice, network data are often collected by querying nodes about their connections. In…

Besides the complexity in time or in number of messages, a common approach for analyzing distributed algorithms is to look at the assumptions they make on the underlying network. We investigate this question from the perspective of network…

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…

Many network systems are composed of interdependent but distinct types of interactions, which cannot be fully understood in isolation. These different types of interactions are often represented as layers, attributes on the edges or as a…

The problem of reliability of a large distributed system is analyzed via a new mathematical model. A typical framework is a system where a set of files are duplicated on several data servers. When one of these servers breaks down, all…

Network reliability is a well-studied problem that requires to measure the probability that a target node is reachable from a source node in a probabilistic (or uncertain) graph, i.e., a graph where every edge is assigned a probability of…

This article explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is…

The mechanisms by which modularity emerges in complex networks are not well understood but recent reports have suggested that modularity may arise from evolutionary selection. We show that finding the modularity of a network is analogous to…

We propose an automatable data-driven methodology for robust nonlinear reduced-order modelling from time-resolved snapshot data. In the kinematical coarse-graining, the snapshots are clustered into few centroids representable for the whole…

Stochastic blockmodels allow us to represent networks in terms of a latent community structure, often yielding intuitions about the underlying social structure. Typically, this structure is inferred based only on a binary network…

Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks, exponential random graph models are a…

This paper is concerned with cross-sectional dependence arising because observations are interconnected through an observed network. Following Doukhan and Louhichi (1999), we measure the strength of dependence by covariances of nonlinearly…

Latent space models for network data characterize each node through a vector of latent features whose pairwise similarities define the edge probabilities among the pairs of nodes. Although this formulation has led to successful…

Many real-world networks known as attributed networks contain two types of information: topology information and node attributes. It is a challenging task on how to use these two types of information to explore structural regularities. In…

Several networks occurring in real life have modular structures that are arranged in an hierarchical fashion. In this paper, we have proposed a model for such networks, using a stochastic generation method. Using this model we show that,…

Large scale real-world network data such as social and information networks are ubiquitous. The study of such social and information networks seeks to find patterns and explain their emergence through tractable models. In most networks, and…

One of the first steps in applications of statistical network analysis is frequently to produce summary charts of important features of the network. Many of these features take the form of sequences of graph statistics counting the number…

Casting neural networks in generative frameworks is a highly sought-after endeavor these days. Contemporary methods, such as Generative Adversarial Networks, capture some of the generative capabilities, but not all. In particular, they lack…

We propose and analyze a stochastic model which explains, analytically, the cutoff behavior of real scale-free networks previously modeled computationally by Amaral et al. [Proc. Natl. Acad. Sci. U.S.A. 97, 11149 (2000)] and others. We…

The stochastic block model is able to generate different network partitions, ranging from traditional assortative communities to disassortative structures. Since the degree-corrected stochastic block model does not specify which mixing…