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Deep generative models (DGMs) for graphs achieve impressively high expressive power thanks to very efficient and scalable neural networks. However, these networks contain non-linearities that prevent analytical computation of many standard…
Exchangeable models for countable vertex-labeled graphs cannot replicate the large sample behaviors of sparsity and power law degree distribution observed in many network datasets. Out of this mathematical impossibility emerges the question…
Random graph (RG) models play a central role in the complex networks analysis. They help to understand, control, and predict phenomena occurring, for instance, in social networks, biological networks, the Internet, etc. Despite a large…
In this paper, we study sparse signal detection problems in Degree Corrected Exponential Random Graph Models (ERGMs). We study the performance of two tests based on the conditionally centered sum of degrees and conditionally centered…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
Understanding which system structure can sustain stable dynamics is a fundamental step in the design and analysis of large scale dynamical systems. Towards this goal, we investigate here the structural stability of systems with a random…
Recurrent Neural Networks (RNNs) are among the most successful machine learning models for sequence modelling, but tend to suffer from an exponential increase in the number of parameters when dealing with large multidimensional data. To…
Random walk neural networks (RWNNs) have emerged as a promising approach for graph representation learning, leveraging recent advances in sequence models to process random walks. However, under realistic sampling constraints, RWNNs often…
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational…
Most real-world networks are noisy and incomplete samples from an unknown target distribution. Refining them by correcting corruptions or inferring unobserved regions typically improves downstream performance. Inspired by the impressive…
Based on Jaynes' maximum entropy principle, exponential random graphs provide a family of principled models that allow the prediction of network properties as constrained by empirical data (observables). However, their use is often hindered…
A common model for social networks are Geometric Inhomogeneous Random Graphs (GIRGs), in which vertices draw a random position in some latent geometric space, and the probability of two vertices forming an edge depends on their geometric…
In this paper, we study the entropy of a hard random geometric graph (RGG), a commonly used model for spatial networks, where the connectivity is governed by the distances between the nodes. Formally, given a connection range $r$, a hard…
Many network datasets exhibit connectivity with variance by resolution and large-scale organization that coexists with localized departures. When vertices have observed ordering or embedding, such as geography in spatial and village…
Deep Markov models (DMM) are generative models that are scalable and expressive generalization of Markov models for representation, learning, and inference problems. However, the fundamental stochastic stability guarantees of such models…
Graph neural networks (GNNs) are powerful machine learning models for various graph learning tasks. Recently, the limitations of the expressive power of various GNN models have been revealed. For example, GNNs cannot distinguish some…
It is desirable for statistical models to detect signals of interest independently of their position. If the data is generated by some smooth process, this additional structure should be taken into account. We introduce a new class of…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
The two-star random graph is the simplest exponential random graph model with nontrivial interactions between the graph edges. We propose a set of auxiliary variables that control the thermodynamic limit where the number of vertices N tends…