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When dealing with spreading processes on networks it can be of the utmost importance to test the reliability of data and identify potential unobserved spreading paths. In this paper we address these problems and propose methods for hidden…

Hypergraphs are widely adopted tools to examine systems with higher-order interactions. Despite recent advancements in methods for community detection in these systems, we still lack a theoretical analysis of their detectability limits.…

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…

We develop a tractable identification approach for strategic network formation models with both strategic link interdependence and individual unobserved heterogeneity (fixed effects). The key challenge is that endogenous network statistics…

Community detection is a fundamental problem in network analysis, with applications in many diverse areas. The stochastic block model is a common tool for model-based community detection, and asymptotic tools for checking consistency of…

In this paper, we introduce a hierarchical extension of the stochastic blockmodel to identify multilevel community structures in networks. We also present a Markov chain Monte Carlo (MCMC) and a variational Bayes algorithm to fit the model…

Network embedding is a fervid topic in current networks science and observes that most real complex systems can be embedded in hidden metrics space and emerge as the geometrical property, where the geometric distance between nodes…

Identifying and explaining the structure of complex networks at different scales has become an important problem across disciplines. At the mesoscale, modular architecture has attracted most of the attention. At the macroscale, other…

Community structure is one of the most relevant features encountered in numerous real-world applications of networked systems. Despite the tremendous effort of scientists working on this subject over the past few decades to characterize,…

Networks are widely used in the biological, physical, and social sciences as a concise mathematical representation of the topology of systems of interacting components. Understanding the structure of these networks is one of the outstanding…

Analysis of degree-degree dependencies in complex networks, and their impact on processes on networks requires null models, i.e. models that generate uncorrelated scale-free networks. Most models to date however show structural negative…

Real-world networks usually have community structure, that is, nodes are grouped into densely connected communities. Community detection is one of the most popular and best-studied research topics in network science and has attracted…

In recent years, machine learning has been adopted to complex networks, but most existing works concern about the structural properties. To use machine learning to detect phase transitions and accurately identify the critical transition…

The design of reliable indicators to anticipate critical transitions in complex systems is an im portant task in order to detect a coming sudden regime shift and to take action in order to either prevent it or mitigate its consequences. We…

Percolation, the formation of a macroscopic connected component, is a key feature in the description of complex networks. The dynamical properties of a variety of systems can be understood in terms of percolation, including the robustness…

The detection of phase transitions is a fundamental challenge in condensed matter physics, traditionally addressed through analytical methods and direct numerical simulations. In recent years, machine learning techniques have emerged as…

Recent decades have seen the discovery of numerous complex materials. At the root of the complexity underlying many of these materials lies a large number of possible contending atomic- and larger-scale configurations and the intricate…

Networks are useful representations of many systems with interacting entities, such as social, biological and physical systems. Characterizing the meso-scale organization, i.e. the community structure, is an important problem in network…

Most real-world networks evolve over time. Existing literature proposes models for dynamic networks that are either unlabeled or assumed to have a single membership structure. On the other hand, a new family of Mixed Membership Stochastic…

We study networks that display community structure -- groups of nodes within which connections are unusually dense. Using methods from random matrix theory, we calculate the spectra of such networks in the limit of large size, and hence…