Concept

Dual graph

Related publications (31)

The connection of the acyclic disconnection and feedback arc sets - On an open problem of Figueroa et al

We examine the connection of two graph parameters, the size of a minimum feedback arcs set and the acyclic disconnection. A feedback arc set of a directed graph is a subset of arcs such that after deletion the graph becomes acyclic. The acyclic disconnecti ...

Elsevier2024

The Power of Two Matrices in Spectral Algorithms for Community Recovery

Colin Peter Sandon

Spectral algorithms are some of the main tools in optimization and inference problems on graphs. Typically, the graph is encoded as a matrix and eigenvectors and eigenvalues of the matrix are then used to solve the given graph problem. Spectral algorithms ...

Ieee-Inst Electrical Electronics Engineers Inc2024

Non-planarity of Markoff graphs mod p

Matthew De Courcy-Ireland

We prove the non-planarity of a family of 3-regular graphs constructed from the solutions to the Markoff equation x2 + y2 + z2 = xyz modulo prime numbers greater than 7. The proof uses Euler characteristic and an enumeration of the short cycles in these gr ...

European Mathematical Soc-Ems2024

DiGress: Discrete Denoising diffusion for graph generation

Pascal Frossard, Volkan Cevher, Igor Krawczuk, Clément Arthur Yvon Vignac, Bohan Wang

This work introduces DiGress, a discrete denoising diffusion model for generating graphs with categorical node and edge attributes. Our model utilizes a discrete diffusion process that progressively edits graphs with noise, through the process of adding or ...

2023

Equivariant Neural Architectures for Representing and Generating Graphs

Clément Arthur Yvon Vignac

Graph machine learning offers a powerful framework with natural applications in scientific fields such as chemistry, biology and material sciences. By representing data as a graph, we encode the prior knowledge that the data is composed of a set of entiti ...

EPFL2023

Fast Parallel Algorithms for Enumeration of Simple, Temporal, and Hop-constrained Cycles

Paolo Ienne, Kubilay Atasu, Jovan Blanusa

Cycles are one of the fundamental subgraph patterns and being able to enumerate them in graphs enables important applications in a wide variety of fields, including finance, biology, chemistry, and network science. However, to enable cycle enumeration in r ...

Assoc Computing Machinery2023

Unsupervised Graph Representation Learning with Cluster-aware Self-training and Refining

Yichen Xu, Qiang Liu

Unsupervised graph representation learning aims to learn low-dimensional node embeddings without supervision while preserving graph topological structures and node attributive features. Previous Graph Neural Networks (GNN) require a large number of labeled ...

Assoc Computing Machinery2023

A Unified Experiment Design Approach for Cyclic and Acyclic Causal Models

Negar Kiyavash, Ehsan Mokhtarian, Saber Salehkaleybar

We study experiment design for unique identification of the causal graph of a system where the graph may contain cycles. The presence of cycles in the structure introduces major challenges for experiment design as, unlike acyclic graphs, learning the skele ...

2023

Graph Embedding for Retrieval

Chi Thang Duong

Information retrieval (IR) systems such as search engines are important for people to find what they need among the tremendous amount of data available in their organization or on the Internet. These IR systems enable users to search in a large data collec ...

EPFL2022

SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators

Andreas Loukas, Nathanaël Perraudin

We approach the graph generation problem from a spectral perspective by first generating the dominant parts of the graph Laplacian spectrum and then building a graph matching these eigenvalues and eigenvectors. Spectral conditioning allows for direct model ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2022

Random walks and forbidden minors III: poly(d epsilon(-1))-time partition oracles for minor-free graph classes

Akash Kumar

Consider the family of bounded degree graphs in any minor-closed family (such as planar graphs). Let d be the degree bound and n be the number of vertices of such a graph. Graphs in these classes have hyperfinite decompositions, where, one removes a small ...

IEEE COMPUTER SOC2022

Tree-cotree decomposition of isogeometric mortared spaces in H(curl) on multi-patch domains

Rafael Vazquez Hernandez, Bernard Kapidani

When applying isogeometric analysis to engineering problems, one often deals with multi-patch spline spaces that have incompatible discretisations, e.g. in the case of moving objects. In such cases mortaring has been shown to be advantageous. This contribu ...

2022

Opinion Formation over Adaptive Networks

Virginia Bordignon

An adaptive network consists of multiple communicating agents, equipped with sensing and learning abilities that allow them to extract meaningful information from measurements. The objective of the network is to solve a global inference problem in a decent ...

EPFL2022

A Topological characterisation of Weisfeiler-Leman equivalence classes

Jacob Max Bamberger

Graph Neural Networks (GNNs) are learning models aimed at processing graphs and signals on graphs. The most popular and successful GNNs are based on message passing schemes. Such schemes inherently have limited expressive power when it comes to distinguish ...

2022

Graph Representation Learning with Optimal Transport: Analysis and Applications

Effrosyni Simou

In several machine learning settings, the data of interest are well described by graphs. Examples include data pertaining to transportation networks or social networks. Further, biological data, such as proteins or molecules, lend themselves well to graph- ...

EPFL2022

Quadratic serendipity element shape functions on general planar polygons

Xiaodong Wei

This paper proposes a method for the construction of quadratic serendipity element (QSE) shape functions on planar convex and concave polygons. Existing approaches for constructing QSE shape functions are linear combinations of the pair-wise products of ge ...

ELSEVIER SCIENCE SA2022

On the robustness of the metric dimension of grid graphs to adding a single edge

Patrick Thiran, Gergely Odor

The metric dimension (MD) of a graph is a combinatorial notion capturing the minimum number of landmark nodes needed to distinguish every pair of nodes in the graph based on graph distance. We study how much the MD can increase if we add a single edge to t ...

2022

Data-driven and Safe Networked Control with Applications to Microgrids

Mustafa Sahin Turan

Today, automatic control is integrated into a wide spectrum of real-world systems such as electrical grids and transportation networks. Many of these systems comprise numerous interconnected agents, perform safety-critical operations, or generate large amo ...

EPFL2022

Belief Control Strategies for Interactions Over Weakly-Connected Graphs

Ali H. Sayed, Bicheng Ying

In diffusion social learning over weakly-connected graphs, it has been shown recently that influential agents shape the beliefs of non-influential agents. This paper analyzes this mechanism more closely and addresses two main questions. First, the article ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

Propagation on Multi-relational Graphs for Node Regression

Eda Bayram

Recent years have witnessed a rise in real-world data captured with rich structural information that can be conveniently depicted by multi-relational graphs. While inference of continuous node features across a simple graph is rather under-studied by the c ...

Springer, Cham2022