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We introduce a method for the theoretical analysis of exponential random graph models. The method is based on a large-deviations approximation to the normalizing constant shown to be consistent using theory developed by Chatterjee and…

Analysis of networks and in particular discovering communities within networks has been a focus of recent work in several fields, with applications ranging from citation and friendship networks to food webs and gene regulatory networks.…

This paper has been withdrawn by the author because there are some typos in proofs.

Link prediction is one of the fundamental problems in network analysis. In many applications, notably in genetics, a partially observed network may not contain any negative examples of absent edges, which creates a difficulty for many…

This article is withdrawn because of a mistake in the main result of the paper.

This paper has been withdrawn by the author(s) in the light of several other works available and due to a misunderstanding in the authorships.

In our recent works, we developed a probabilistic framework for structural analysis in undirected networks. The key idea of that framework is to sample a network by a symmetric bivariate distribution and then use that bivariate distribution…

This paper has been withdrawn by the author; a revised version is part of the author's phd-thesis "Quasi-logarithmic structures" (Zurich, 2007).

Social networks often encode community structure using multiple distinct types of links between nodes. In this paper we introduce a novel method to extract information from such multi-layer networks, where each type of link forms its own…

Consider observations $y_1,\dots,y_n$ on nodes of a connected graph, where the $y_i$ independently come from $N(\theta_i, \sigma^2)$ distributions and an unknown partition divides the $n$ observations into blocks. One well-studied class of…

This paper has been withdrawn by the authors as they feel it inappropriate to publish this paper for the time being.

We introduce an architecture based on deep hierarchical decompositions to learn effective representations of large graphs. Our framework extends classic R-decompositions used in kernel methods, enabling nested part-of-part relations. Unlike…

Graph Neural Networks (GNNs) have achieved notable success in the analysis of non-Euclidean data across a wide range of domains. However, their applicability is constrained by the dependence on the observed graph structure. To solve this…

In this paper we examine a variant of the voter model on a dynamically changing network where agents have the option of changing their friends rather than changing their opinions. We analyse, in the context of dense random graphs, two…

The ideas of aleatoric and epistemic uncertainty are widely used to reason about the probabilistic predictions of machine-learning models. We identify incoherence in existing discussions of these ideas and suggest this stems from the…

When a network is reconstructed from data, two types of errors can occur: false positive and false negative errors about the presence or absence of links. In this paper, the vertex degree distribution of the true underlying network is…

Many complex systems change their structure over time, in these cases dynamic networks can provide a richer representation of such phenomena. As a consequence, many inference methods have been generalized to the dynamic case with the aim to…

Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on…

We study the network untangling problem introduced by Rozenshtein, Tatti, and Gionis [DMKD 2021], which is a variant of Vertex Cover on temporal graphs -- graphs whose edge set changes over discrete time steps. They introduce two problem…

Many models are put forward to mimic the evolution of real networked systems. A well-accepted way to judge the validity is to compare the modeling results with real networks subject to several structural features. Even for a specific real…