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Graph generation aims to sample discrete node and edge attributes while satisfying coupled structural constraints. Diffusion models for graphs often adopt largely factorized forward-noising, and many flow-matching methods start from…
A stochastic model relating the parameters of astrophysical structures to the parameters of their granular components is applied to the formation of hierarchical, large-scale structures from galaxies assumed as point-like objects. If the…
Graphs are naturally used to describe the structures of various real-world systems in biology, society, computer science etc., where subgraphs or motifs as basic blocks play an important role in function expression and information…
Graphs have been widely adopted to denote structural connections between entities. The relations are in many cases heterogeneous, but entangled together and denoted merely as a single edge between a pair of nodes. For example, in a social…
In this paper we define a new class of weighted complex networks sharing several properties with fractal sets, and whose topology can be completely analytically characterized in terms of the involved parameters and of the fractal dimension.…
Understanding the intricate architecture of brain networks and its connection to brain function is essential for deciphering the underlying principles of cognition and disease. While traditional graph-theoretical measures have been widely…
Gaussian Graphical Models (GGMs) are popular tools for studying network structures. However, many modern applications such as gene network discovery and social interactions analysis often involve high-dimensional noisy data with outliers or…
Graphs are a powerful data structure for representing relational data and are widely used to describe complex real-world systems. Probabilistic Graphical Models (PGMs) and Graph Neural Networks (GNNs) can both leverage graph-structured…
This paper presents a versatile model for generating fractal complex networks that closely mirror the properties of real-world systems. By combining features of reverse renormalization and evolving network models, the proposed approach…
When characterizing materials, it can be important to not only predict their mechanical properties, but also to estimate the probability distribution of these properties across a set of samples. Constitutive neural networks allow for the…
Graph neural networks (GNNs), especially dynamic GNNs, have become a research hotspot in spatio-temporal forecasting problems. While many dynamic graph construction methods have been developed, relatively few of them explore the causal…
This paper introduces a scale-invariant methodology employing \textit{Fractal Geometry} to analyze and explain the nonlinear dynamics of complex connectionist systems. By leveraging architectural self-similarity in Deep Neural Networks…
Graph condensation (GC), which reduces the size of a large-scale graph by synthesizing a small-scale condensed graph as its substitution, has benefited various graph learning tasks. However, existing GC methods rely on centralized data…
The mining and exploitation of graph structural information have been the focal points in the study of complex networks. Traditional structural measures in Network Science focus on the analysis and modelling of complex networks from the…
Representation learning over graph structure data has been widely studied due to its wide application prospects. However, previous methods mainly focus on static graphs while many real-world graphs evolve over time. Modeling such evolution…
Gaussian processes (GPs) are an attractive class of machine learning models because of their simplicity and flexibility as building blocks of more complex Bayesian models. Meanwhile, graph neural networks (GNNs) emerged recently as a…
This paper introduces Polynomial Graphical Lasso (PGL), a new approach to learning graph structures from nodal signals. Our key contribution lies in modeling the signals as Gaussian and stationary on the graph, enabling the development of a…
We introduce the Distributed-order fRActional Graph Operating Network (DRAGON), a novel continuous Graph Neural Network (GNN) framework that incorporates distributed-order fractional calculus. Unlike traditional continuous GNNs that utilize…
In most domains of network analysis researchers consider networks that arise in nature with weighted edges. Such networks are routinely dichotomized in the interest of using available methods for statistical inference with networks. The…
This paper proposes a data-driven graphical framework for the real-time search of risky cascading fault chains (FCs). While identifying risky FCs is pivotal to alleviating cascading failures, the complex spatio-temporal dependencies among…