Related papers: A General Solution for Network Models with Pairwis…

It is shown how exactly solved edge interaction models on the square lattice, may be extended onto more general planar graphs, with edges connecting a subset of next nearest neighbour vertices of $\mathbb{Z}^3$. This is done by using local…

Generation of deviates from random graph models with non-trivial edge dependence is an increasingly important problem. Here, we introduce a method which allows perfect sampling from random graph models in exponential family form…

Joint extraction of entities and relations aims to detect entity pairs along with their relations using a single model. Prior work typically solves this task in the extract-then-classify or unified labeling manner. However, these methods…

Describing the collective activity of neural populations is a daunting task: the number of possible patterns grows exponentially with the number of cells, resulting in practically unlimited complexity. Recent empirical studies, however,…

Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…

We consider the class of graphs for which the edge connectivity is equal to the maximum number of edge-disjoint spanning trees, and the natural generalization to matroids, where the cogirth is equal to the number of disjoint bases. We…

We review mathematically tractable models for connected networks on random points in the plane, emphasizing the class of proximity graphs which deserves to be better known to applied probabilists and statisticians. We introduce and motivate…

Multiplex graphs capture diverse relations among shared nodes. Most predictors either collapse layers or treat them independently. This loses crucial inter-layer dependencies and struggles with scalability. To overcome this, we frame…

Desirable random graph models (RGMs) should (i) reproduce common patterns in real-world graphs (e.g., power-law degrees, small diameters, and high clustering), (ii) generate variable (i.e., not overly similar) graphs, and (iii) remain…

In this paper, we investigate optimal control of network-coupled subsystems where the dynamics and the cost couplings depend on an underlying undirected weighted graph. The graph coupling matrix in the dynamics may be the adjacency matrix,…

This paper considers learning a product graph from multi-attribute graph signals. Our work is motivated by the widespread presence of multilayer networks that feature interactions within and across graph layers. Focusing on a product graph…

Random tensor models are generalizations of random matrix models which admit $1/N$ expansions. In this article we show that the topological recursion, a modern approach to matrix models which solves the loop equations at all orders, is also…

We introduce a new distributed algorithm for aligning graphs or finding substructures within a given graph. It is based on the cavity method and is used to study the maximum-clique and the graph-alignment problems in random graphs. The…

To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…

Time-continuous dynamical systems defined on graphs are often used to model complex systems with many interacting components in a non-spatial context. In the reverse sense attaching meaningful dynamics to given 'interaction diagrams' is a…

Random unimodular lattice triangulations have been recently used as an embedded random graph model, which exhibit a crossover behaviour between an ordered, large-world and a disordered, small-world behaviour. Using the ergodic Pachner flips…

Comparing networks is essential for a number of downstream tasks, from clustering to anomaly detection. Despite higher-order interactions being critical for understanding the dynamics of complex systems, traditional approaches for network…

Network systems consist of subsystems and their interconnections, and provide a powerful framework for analysis, modeling and control of complex systems. However, subsystems may have high-dimensional dynamics, and the amount and nature of…

Graph machine learning models have been successfully deployed in a variety of application areas. One of the most prominent types of models - Graph Neural Networks (GNNs) - provides an elegant way of extracting expressive node-level…

Learning the undirected graph structure of a Markov network from data is a problem that has received a lot of attention during the last few decades. As a result of the general applicability of the model class, a myriad of methods have been…