相关论文: Distance-layer structure of the De Bruijn and Kaut…
Representing various networked data as multiplex networks, networks of networks and other multilayer networks can reveal completely new types of structures in these system. We introduce a general and principled graphlet framework for…
A Delaunay graph built on a planar point set has an edge between two vertices when there exists a disk with the two vertices on its boundary and no vertices in its interior. When the disk is replaced with an equilateral triangle, the…
The structural analysis of shape boundaries leads to the characterization of objects as well as to the understanding of shape properties. The literature on graphs and networks have contributed to the structural characterization of shapes…
For a given point set $S$ in a plane, we develop a distributed algorithm to compute the $\alpha-$shape of $S$. $\alpha-$shapes are well known geometric objects which generalize the idea of a convex hull, and provide a good definition for…
Detecting structure in data is the first step to arrive at meaningful representations for systems. This is particularly challenging for dislocation networks evolving as a consequence of plastic deformation of crystalline systems. Our study…
High triangle density -- the graph property stating that a constant fraction of two-hop paths belong to a triangle -- is a common signature of social networks. This paper studies triangle-dense graphs from a structural perspective. We prove…
Complex systems are made up of many interacting components. Network science provides the tools to analyze and understand these interactions. Community detection is a key technique in network science for uncovering the structures that shape…
We introduce a decomposition method for the distributed calculation of exact Euclidean Minimum Spanning Trees in high dimensions (where sub-quadratic algorithms are not effective), or more generalized geometric-minimum spanning trees of…
In this paper, we propose DeMuon, a method for decentralized matrix optimization over a given communication topology. DeMuon incorporates matrix orthogonalization via Newton-Schulz iterations-a technique inherited from its centralized…
It is well-known since the seventies of last century that Depth First Search (DFS) can be used to compute strongly connected components [RE. Tarjan. SIAM Journal on Computing, 1972] and Breadth First Search (BFS) can be used to compute…
Graph neural networks (GNNs) are widely used in the applications based on graph structured data, such as node classification and link prediction. However, GNNs are often used as a black-box tool and rarely get in-depth investigated…
The Kautz digraphs $K(d,\ell)$ are a well-known family of dense digraphs, widely studied as a good model for interconnection networks. Closely related to these, the cyclic Kautz digraphs $CK(d,\ell)$ were recently introduced by B\"ohmov\'a,…
U-Nets are among the most widely used architectures in computer vision, renowned for their exceptional performance in applications such as image segmentation, denoising, and diffusion modeling. However, a theoretical explanation of the…
A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…
In this paper, we present an algorithm for evaluating lexical similarity between a given language and several reference language clusters. As an input, we have a list of concepts and the corresponding translations in all considered…
Unsupervised pretraining and dropout have been well studied, especially with respect to regularization and output consistency. However, our understanding about the explicit convergence rates of the parameter estimates, and their dependence…
Graph Neural Networks (GNNs) are characterized by their capacity of processing graph-structured data. However, due to the sparsity of labels under semi-supervised learning, they have been found to exhibit biased performance on specific…
Whether comparing networks to each other or to random expectation, measuring dissimilarity is essential to understanding the complex phenomena under study. However, determining the structural dissimilarity between networks is an ill-defined…
We investigate the structure of graphs of twin-width at most $1$, and obtain the following results: - Graphs of twin-width at most $1$ are permutation graphs. In particular they have an intersection model and a linear structure. - There is…
We introduce a new language to describe the geometry of affine Deligne-Lusztig varieties in affine flag varieties. This second part of a two paper series uses this new language, i.e. the double Bruhat graph, to describe certain structure…