Related papers: Regular decomposition of large graphs and other st…
The characteristic sequence of hypergraphs $<P_n : n<\omega>$ associated to a formula $\phi(x;y)$, introduced in [arXiv:0908.4111], is defined by $P_n(y_1,... y_n) = (\exists x) \bigwedge_{i\leq n} \phi(x;y_i)$. This paper continues the…
Our research integrates graph data with Large Language Models (LLMs), which, despite their advancements in various fields using large text corpora, face limitations in encoding entire graphs due to context size constraints. This paper…
Community detection is a fundamental task in graph analysis, with methods often relying on fitting models like the Stochastic Block Model (SBM) to observed networks. While many algorithms can accurately estimate SBM parameters when the…
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 learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying…
A Random SubMatrix method (RSM) is proposed to calculate the low-rank decomposition of large-scale matrices with known entry percentage \rho. RSM is very fast as the floating-point operations (flops) required are compared favorably with the…
Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…
We present an exact algorithm for computing all common subgraphs with the maximum number of vertices across multiple graphs. Our approach is further extended to handle the connected Maximum Common Subgraph (MCS), identifying the largest…
Large Language Models (LLMs) have demonstrated strong potential for many mathematical problems. However, their performance on graph algorithmic tasks is still unsatisfying, since graphs are naturally more complex in topology and often…
Recently, network embedding that encodes structural information of graphs into a vector space has become popular for network analysis. Although recent methods show promising performance for various applications, the huge sizes of graphs may…
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…
The Weisfeiler-Leman (WL) dimension is an established measure for the inherent descriptive complexity of graphs and relational structures. It corresponds to the number of variables that are needed and sufficient to define the object of…
Graphs are now ubiquitous in almost every field of research. Recently, new research areas devoted to the analysis of graphs and data associated to their vertices have emerged. Focusing on dynamical processes, we propose a fast, robust and…
In this manuscript we develop a version of Szemer\'edi's regularity lemma that is suitable for analyzing multicolorings of complete graphs and directed graphs. In this, we follow the proof of Alon, Fischer, Krivelevich and M. Szegedy…
In many models for large-scale computation, decomposition of the problem is key to efficient algorithms. For distance-related graph problems, it is often crucial that such a decomposition results in clusters of small diameter, while the…
The enormous amount of data to be represented using large graphs exceeds in some cases the resources of a conventional computer. Edges in particular can take up a considerable amount of memory as compared to the number of nodes. However,…
Estimating graphical model structure from high-dimensional and undersampled data is a fundamental problem in many scientific fields. Existing approaches, such as GLASSO, latent variable GLASSO, and latent tree models, suffer from high…
We study online robust matrix completion on graphs. At each iteration a vector with some entries missing is revealed and our goal is to reconstruct it by identifying the underlying low-dimensional subspace from which the vectors are drawn.…
A classic approach in dynamical systems is to use particular geometric structures to deduce statistical properties, for example the existence of invariant measures with stochastic-like behaviour such as large deviations or decay of…
Classical graph algorithms work well for combinatorial problems that can be thoroughly formalized and abstracted. Once the algorithm is derived, it generalizes to instances of any size. However, developing an algorithm that handles complex…