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A {\em faithful (unit) distance graph} in $\mathbb{R}^d$ is a graph whose set of vertices is a finite subset of the $d$-dimensional Euclidean space, where two vertices are adjacent if and only if the Euclidean distance between them is…
This paper considers *-graphs in which all vertices have degree 4 or 6, and studies the question of calculating the genus of orientable 2-surfaces into which such graphs may be embedded. A *-graph is a graph endowed with a formal adjacency…
Any symmetric affinity function $w: V\times V \to \mathbb{R}_+$ defined on a discrete set $V$ induces Euclidean space structure on $V$. In particular, an undirected graph specified by an affinity (or adjacency) matrix can be considered as a…
Graph embedding methods transform high-dimensional and complex graph contents into low-dimensional representations. They are useful for a wide range of graph analysis tasks including link prediction, node classification, recommendation and…
We propose a new method for embedding graphs while preserving directed edge information. Learning such continuous-space vector representations (or embeddings) of nodes in a graph is an important first step for using network information…
Network embedding is a fervid topic in current networks science and observes that most real complex systems can be embedded in hidden metrics space and emerge as the geometrical property, where the geometric distance between nodes…
We introduce and study embeddings of graphs in finite projective planes, and present related results for some families of graphs including complete graphs and complete bipartite graphs. We also make connections between embeddings of graphs…
Several approaches have been developed that generate embeddings for Description Logic ontologies and use these embeddings in machine learning. One approach of generating ontologies embeddings is by first embedding the ontologies into a…
Graph representation learning plays an important role in many graph mining applications, but learning embeddings of large-scale graphs remains a problem. Recent works try to improve scalability via graph summarization -- i.e., they learn…
We prove estimates for the optimal volume of thick embeddings of finite graphs into symmetric spaces, generalising results of Kolmogorov-Barzdin and Gromov-Guth for embeddings into Euclidean spaces. We distinguish two very different…
In the past few years, the study of receptive field codes has been of large interest to mathematicians. Here we give a complete characterization of receptive field codes realizable by connected receptive fields and we give the minimal…
Relational representation learning has lately received an increase in interest due to its flexibility in modeling a variety of systems like interacting particles, materials and industrial projects for, e.g., the design of spacecraft. A…
We study the problem of inducing interpretability in KG embeddings. Specifically, we explore the Universal Schema (Riedel et al., 2013) and propose a method to induce interpretability. There have been many vector space models proposed for…
Knowledge graph embedding has recently become a popular way to model relations and infer missing links. In this paper, we present a group theoretical perspective of knowledge graph embedding, connecting previous methods with different group…
Every graph G can be embedded in a Euclidean space as a two-distance set. This allows us to reformulate the analogue of Borsuk's conjecture for two-distance sets in terms of graphs. This conjecture remains open for dimensions from 4 to 63.…
It is shown that a simple graph which is embeddable in the real projective plane is minimally 3-rigid if and only if it is (3,6)-tight. Moreover the topologically uncontractible embedded graphs of this type are constructible from one of 8…
Network embedding, which aims to learn low-dimensional representations of nodes, has been used for various graph related tasks including visualization, link prediction and node classification. Most existing embedding methods rely solely on…
We define a special case of tree decompositions for planar graphs that respect a given embedding of the graph. We study the analogous width of the resulting decomposition we call the embedded-width of a plane graph. We show both upper…
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…
Measuring meaning is a central problem in cultural sociology and word embeddings may offer powerful new tools to do so. But like any tool, they build on and exert theoretical assumptions. In this paper I theorize the ways in which word…