Related papers: Theories of Hypergraph-Graph (HG(2)) Data Structur…
A speculative overview of a future topic of research. The paper is a collection of ideas concerning two related areas: 1) Graph computation machines ("computing with graphs"). This is the class of models of computation in which the state of…
Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…
Hypergraphs capture multi-way relationships in data, and they have consequently seen a number of applications in higher-order network analysis, computer vision, geometry processing, and machine learning. In this paper, we develop…
Graphs have been utilized as a powerful tool to model pairwise relationships between people or objects. Such structure is a special type of a broader concept referred to as hypergraph, in which each hyperedge may consist of an arbitrary…
In this paper, we present a hypergraph neural networks (HGNN) framework for data representation learning, which can encode high-order data correlation in a hypergraph structure. Confronting the challenges of learning representation for…
We study the implications of the modeling choice to use a graph, instead of a hypergraph, to represent real-world interconnected systems whose constituent relationships are of higher order by nature. Such a modeling choice typically…
In this paper, we propose a novel hypergraph based method (called HF) to fit and segment multi-structural data. The proposed HF formulates the geometric model fitting problem as a hypergraph partition problem based on a novel hypergraph…
We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…
Graph representation learning (a.k.a. network embedding) is a significant topic of network analysis, due to its effectiveness to support various graph inference tasks. In this paper, we study the representation learning with multiple…
We propose a novel structure, the data-sharing graph, for characterizing sharing patterns in large-scale data distribution systems. We analyze this structure in two such systems and uncover small-world patterns for data-sharing…
There is increasing focus on analyzing data represented as hypergraphs, which are better able to express complex relationships amongst entities than are graphs. Much of the critical information about hypergraph structure is available only…
Knowledge Graph (KG) is a graph based data structure to represent facts of the world where nodes represent real world entities or abstract concept and edges represent relation between the entities. Graph as representation for knowledge has…
Hypergraphs play a pivotal role in the modelling of data featuring higher-order relations involving more than two entities. Hypergraph neural networks emerge as a powerful tool for processing hypergraph-structured data, delivering…
Most previous heterogeneous graph embedding models represent elements in a heterogeneous graph as vector representations in a low-dimensional Euclidean space. However, because heterogeneous graphs inherently possess complex structures, such…
While network science has become an indispensable tool for studying complex systems, the conventional use of pairwise links often shows limitations in describing high-order interactions properly. Hypergraphs, where each edge can connect…
Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…
Heterogeneous graphs (HGs) also known as heterogeneous information networks have become ubiquitous in real-world scenarios; therefore, HG embedding, which aims to learn representations in a lower-dimension space while preserving the…
Current distributed data fabrics lack a rigorous mathematical foundation, often relying on ad-hoc architectures that struggle with consistency, lineage, and scale. We propose a mathematical framework for data fabrics, unifying heterogeneous…
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 representation of complex systems as networks is inappropriate for the study of certain problems. We show several examples of social, biological, ecological and technological systems where the use of complex networks gives very limited…