Related papers: Rigid Graph Compression: Motif-based rigidity anal…

Graph condensation (GC) has gained significant attention for its ability to synthesize smaller yet informative graphs. However, existing studies often overlook the robustness of GC in scenarios where the original graph is corrupted. In such…

Random geometric graphs (RGG) can be formalized as hidden-variables models where the hidden variables are the coordinates of the nodes. Here we develop a general approach to extract the typical configurations of a generic hidden-variables…

Graph compression is a data analysis technique that consists in the replacement of parts of a graph by more general structural patterns in order to reduce its description length. It notably provides interesting exploration tools for the…

A $d$-dimensional (bar-and-joint) framework $(G,p)$ consists of a graph $G=(V,E)$ and a realisation $p:V\to \mathbb{R}^d$. It is rigid if every continuous motion of the vertices which preserves the lengths of the edges is induced by an…

The discovery and analysis of network patterns are central to the scientific enterprise. In the present work, we developed and evaluated a new approach that learns the building blocks of graphs that can be used to understand and generate…

Graph neural networks can accurately predict the chemical properties of many molecular systems, but their suitability for large, macromolecular assemblies such as gels is unknown. Here, graph neural networks were trained and optimised for…

Combinatorial rigidity theory seeks to describe the rigidity or flexibility of bar-joint frameworks in R^d in terms of the structure of the underlying graph G. The goal of this article is to broaden the foundations of combinatorial rigidity…

We introduce the \emph{graphical reconfigurable circuits (GRC)} model as an abstraction for distributed graph algorithms whose communication scheme is based on local mechanisms that collectively construct long-range reconfigurable channels…

Graph neural networks (GNNs) have attracted widespread attention for their impressive capability of graph representation learning. However, the increasing prevalence of large-scale graphs presents a significant challenge for GNN training…

Functional structures from across the engineered and biological world combine rigid elements such as bones and columns with flexible ones such as cables, fibers and membranes. These structures are known loosely as tensegrities, since these…

Sparse graphs and their associated matroids play an important role in rigidity theory, where they capture the combinatorics of generically rigid structures. We define a new family called {\bf graded sparse graphs}, arising from generically…

Graph rigidity theory studies the capability of a graph embedded in the Euclidean space to constrain its global geometric shape via local constraints among nodes and edges, and has been widely exploited in network localization and formation…

The notions of $r$-robustness and $(r,s)$-robustness of a network have been earlier introduced in the literature to achieve resilient consensus in the presence of misbehaving agents. However, while higher robustness levels enable networks…

We prove a robust contraction decomposition theorem for $H$-minor-free graphs, which states that given an $H$-minor-free graph $G$ and an integer $p$, one can partition in polynomial time the vertices of $G$ into $p$ sets $Z_1,\dots,Z_p$…

Graphs are a natural representation for systems based on relations between connected entities. Combinatorial optimization problems, which arise when considering an objective function related to a process of interest on discrete structures,…

The increasing share of renewable energy and distributed electricity generation requires the development of deep learning approaches to address the lack of flexibility inherent in traditional power grid methods. In this context, Graph…

Technology trends will cause data movement to account for the majority of energy expenditure and execution time on emerging computers. Therefore, computational complexity will no longer be a sufficient metric for comparing algorithms, and a…

Graph databases have been the subject of significant research and development. Problems such as modularity, centrality, alignment, and clustering have been formalized and solved in various application contexts. In this paper, we focus on…

This paper extends graphic statics by describing the forces and moments in any 3D rigid-jointed frame structure in terms of cell complexes using homology theory of algebraic topology. Graphic statics provides a highly geometric way to…

Graph classification is crucial in network analyses. Networks face potential security threats, such as adversarial attacks. Some defense methods may trade off the algorithm complexity for robustness, such as adversarial training, whereas…