相关论文: Effective Resistance Preserving Directed Graph Sym…
Directed graphs are widely used in modelling of nonsymmetric relations in various sciences and engineering disciplines. We discuss invariants of strongly connected directed graphs - minimal number of vertices or edges necessary to remove to…
Motion planning is a fundamental problem of robotics with applications in many areas of computer science and beyond. Its restriction to graphs has been investigated in the literature for it allows to concentrate on the combinatorial problem…
The Hermitian adjacency matrices of digraphs based on the sixth root of unity were introduced in [B. Mohar, A new kind of Hermitian matrices for digraphs, Linear Alg. Appl. (2020)]. They appear to be the most natural choice for the spectral…
It is reported that dynamical systems over digraphs have superior performance in terms of system damping and tolerance to time delays if the underlying graph Laplacian has a purely real spectrum. This paper investigates the topological…
A realization of a graph $G=(V,E)$ is a map $v\colon V\to\Bbb R^d$ that assigns to each vertex a point in $d$-dimensional Euclidean space. We study graph realizations from the perspective of representation theory (expressing certain…
We define a new family of similarity and distance measures on graphs, and explore their theoretical properties in comparison to conventional distance metrics. These measures are defined by the solution(s) to an optimization problem which…
The notion of resistance distance, introduced by Klein and Randi\'c, has become a fundamental concept in spectral graph theory and network analysis, as it captures both the structural and electrical properties of a graph. The associated…
A directed graph $G=(V,E)$ is {\it strongly pseudo transitive} if there is a partition $\{A,E-A\}$ of $E$ so that graphs $G_1=(V,A)$ and $G_2=(V,E-A)$ are transitive, and additionally, if $ab\in A$ and $bc\in E $ implies that $ac\in E$. A…
In the field of graph signal processing (GSP), directed graphs present a particular challenge for the "standard approaches" of GSP to due to their asymmetric nature. The presence of negative- or complex-weight directed edges, a graphical…
Graph contrastive learning has become a powerful technique for several graph mining tasks. It learns discriminative representation from different perspectives of augmented graphs. Ubiquitous in our daily life, singed-directed graphs are the…
Graph-based representations underlie a wide range of scientific problems. Graph connectivity is typically represented as a sparse matrix in the Compressed Sparse Row format. Large-scale graphs rely on distributed storage, allocating…
We propose the notion of {\it resistance of a graph} as an accompanying notion of the structure entropy to measure the force of the graph to resist cascading failure of strategic virus attacks. We show that for any connected network $G$,…
We introduce and discuss the Minimum Capacity-Preserving Subgraph (MCPS) problem: given a directed graph and a retention ratio $\alpha \in (0,1)$, find the smallest subgraph that, for each pair of vertices $(u,v)$, preserves at least a…
We consider the problem on finding the edge weights that maximize the algebraic connectivity of a graph (smallest positive eigenvalue of the Laplacian), subject to the condition that the total effective resistance is kept constant. We…
This work presents a new method to design consensus controllers for perturbed double integrator systems whose interconnection is described by a directed graph containing a rooted spanning tree. We propose new robust controllers to solve the…
Graph coarsening is a widely used dimensionality reduction technique for approaching large-scale graph machine learning problems. Given a large graph, graph coarsening aims to learn a smaller-tractable graph while preserving the properties…
Graph clustering is a fundamental technique in data analysis with applications in many different fields. While there is a large body of work on clustering undirected graphs, the problem of clustering directed graphs is much less understood.…
In this paper, we study the construction and transformation of two-dimensional persistent graphs. Persistence is a generalization to directed graphs of the undirected notion of rigidity. In the context of moving autonomous agent formations,…
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…
Graph embedding is an effective method to represent graph data in a low dimensional space for graph analytics. Most existing embedding algorithms typically focus on preserving the topological structure or minimizing the reconstruction…