Related papers: On Adjacency and e-Adjacency in General Hypergraph…
Graph and hypergraph representation learning has attracted increasing attention from various research fields. Despite the decent performance and fruitful applications of Graph Neural Networks (GNNs), Hypergraph Neural Networks (HGNNs), and…
In this work, we propose a unified abstraction for graph algorithms: the Extended General Einsums language, or EDGE. The EDGE language expresses graph algorithms in the language of tensor algebra, providing a rigorous, succinct, and…
A complex unit hypergraph is a hypergraph where each vertex-edge incidence is given a complex unit label. We define the adjacency, incidence, Kirchoff Laplacian and normalized Laplacian of a complex unit hypergraph and study each of them.…
There are typically several nonisomorphic graphs having a given degree sequence, and for any two degree sequence terms it is often possible to find a realization in which the corresponding vertices are adjacent and one in which they are…
Scene graph generation aims to produce structured representations for images, which requires to understand the relations between objects. Due to the continuous nature of deep neural networks, the prediction of scene graphs is divided into…
Edge computing is highly demanded to achieve their full potentials Internet of Things (IoT), since various IoT systems have been generating big data facilitating modern latency-sensitive applications. As a basic problem, network dismantling…
View-based approach that recognizes 3D shape through its projected 2D images achieved state-of-the-art performance for 3D shape recognition. One essential challenge for view-based approach is how to aggregate the multi-view features…
Pre-trained language models advance patent classification and retrieval via encoding claims as flat token sequences, yet overlooking the dependency hierarchy among claims. Incorporating the hierarchy into self-attention poses two…
Graph embedding is a powerful method to represent graph neurological data (e.g., brain connectomes) in a low dimensional space for brain connectivity mapping, prediction and classification. However, existing embedding algorithms have two…
Many important real-world applications-such as social networks or distributed data bases-can be modeled as hypergraphs. In such a model, vertices represent entities-such as users or data records-whereas hyperedges model a group membership…
In this paper, we define the adjacency matrix of a semigraph. We give the conditions for a matrix to be semigraphical and give an algorithm to construct a semigraph from the semigraphical matrices. We derive lower and upper bounds for…
Representation learning on heterogeneous graphs aims to obtain meaningful node representations to facilitate various downstream tasks, such as node classification and link prediction. Existing heterogeneous graph learning methods are…
We consider the following definition of connectivity in $k$-uniform hypergraphs: Two $j$-sets are $j$-connected if there is a walk of edges between them such that two consecutive edges intersect in at least $j$ vertices. We determine the…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
Hypergraphs, increasingly utilised for modelling complex and diverse relationships in modern networks, gain much attention representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery is one of the…
Hypergraphs have emerged as a powerful modeling framework to represent systems with multiway interactions, that is systems where interactions may involve an arbitrary number of agents. Here we explore the properties of real-world…
The absence of intrinsic adjacency relations and orientation systems in hypergraphs creates fundamental challenges for constructing sheaf Laplacians of arbitrary degrees. We resolve these limitations through symmetric simplicial sets…
Graph embedding is a transformation of vertices of a graph into set of vectors. Good embeddings should capture the graph topology, vertex-to-vertex relationship, and other relevant information about graphs, subgraphs, and vertices. If these…
Finding inherent or processed links within a dataset allows to discover potential knowledge. The main contribution of this article is to define a global framework that enables optimal knowledge discovery by visually rendering co-occurences…
Network scientists have shown that there is great value in studying pairwise interactions between components in a system. From a linear algebra point of view, this involves defining and evaluating functions of the associated adjacency…