Related papers: (c-)AND: A new graph model
Graph transformers typically embed every node in a single Euclidean space, blurring heterogeneous topologies. We prepend a lightweight Riemannian mixture-of-experts layer that routes each node to various kinds of manifold, mixture of…
We introduce a hypergraph matrix, named the unified matrix, and use it to represent the hypergraph as a graph. We show that the unified matrix of a hypergraph is identical to the adjacency matrix of the associated graph. This enables us to…
Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…
The metric representation of a vertex $u$ in a connected graph $G$ respect to an ordered vertex subset $W=\{\omega_1, \dots , \omega_n\}\subset V(G)$ is the vector of distances $r(u\vert W)=(d(u,\omega_1), \dots , d(u,\omega_n))$. A vertex…
Graphs are ubiquitous data structures for representing interactions between entities. With an emphasis on the use of graphs to represent chemical molecules, we explore the task of learning to generate graphs that conform to a distribution…
Spatial networks are networks whose graph topology is constrained by their embedded spatial space. Understanding the coupled spatial-graph properties is crucial for extracting powerful representations from spatial networks. Therefore,…
Representation learning on graphs has been gaining attention due to its wide applicability in predicting missing links, and classifying and recommending nodes. Most embedding methods aim to preserve certain properties of the original graph…
Various simplicial complexes can be associated with a graph. Box complexes form an important families of such simplicial complexes and are especially useful for providing lower bounds on the chromatic number of the graph via some of their…
Graph-level representations are crucial tools for characterising structural differences between graphs. However, comparing graphs with different cardinalities, even when sampled from the same underlying distribution, remains challenging.…
We study contact representations for graphs, which we call pixel representations in 2D and voxel representations in 3D. Our representations are based on the unit square grid whose cells we call pixels in 2D and voxels in 3D. Two pixels are…
A $d$-box is the cartesian product of $d$ intervals of $\mathbb{R}$ and a $d$-box representation of a graph $G$ is a representation of $G$ as the intersection graph of a set of $d$-boxes in $\mathbb{R}^d$. It was proved by Thomassen in 1986…
Every graph G can be embedded in a Euclidean space as a two-distance set. The Euclidean representation number of G is the smallest dimension in which G is representable by such an embedding. We consider spherical and J-spherical…
Adjacency between two vertices in graphs or hypergraphs is a pairwise relationship. It is redefined in this article as 2-adjacency. In general hypergraphs, hyperedges hold for $n$-adic relationship. To keep the $n$-adic relationship the…
Learning useful representations is a key ingredient to the success of modern machine learning. Currently, representation learning mostly relies on embedding data into Euclidean space. However, recent work has shown that data in some domains…
Molecular graphs generally contain subgraphs (known as groups) that are identifiable and significant in composition, functionality, geometry, etc. Flat latent representations (node embeddings or graph embeddings) fail to represent, and…
A connected digraph in which the in-degree of any vertex equals its out-degree is Eulerian; this baseline result is used as the basis of existence proofs for universal cycles (also known as ucycles or generalized deBruijn cycles or…
Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…
A multifamily set representation of a finite simple graph $G$ is a multifamily $\mathcal{F}$ of sets (not necessarily distinct) for which each set represents a vertex in $G$ and two sets in $\mathcal{F}$ intersects if and only if the two…
This paper considers the problem of embedding directed graphs in Euclidean space while retaining directional information. We model a directed graph as a finite set of observations from a diffusion on a manifold endowed with a vector field.…
Complex networks represented as node adjacency matrices constrains the application of machine learning and parallel algorithms. To address this limitation, network embedding (i.e., graph representation) has been intensively studied to learn…