Related papers: Generalized Word-Representable Graphs
A graph $G=(V,E)$ is representable if there exists a word $W$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $W$ if and only if $(x,y)\in E$ for each $x\neq y$. If $W$ is $k$-uniform (each letter of $W$ occurs exactly $k$…
Attributes of words and relations between two words are central to numerous tasks in Artificial Intelligence such as knowledge representation, similarity measurement, and analogy detection. Often when two words share one or more attributes…
Series-parallel (SP) graphs are binary edge-labeled graphs with a designated source and target vertex, built using serial and parallel composition. A set of graphs is recognizable if membership depends only on its image under a homomorphism…
Representing words by vectors, or embeddings, enables computational reasoning and is foundational to automating natural language tasks. For example, if word embeddings of similar words contain similar values, word similarity can be readily…
Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…
A graph $G=(V,E)$ is said to be word-representable if there exists a word $w$ over the alphabet $V$ such that two distinct letters $x,y\in V$ alternate in $w$ if and only if $xy \in E$. Word-representable graphs form a well-studied graph…
A pair of letters $x$ and $y$ are said to alternate in a word $w$ if, after removing all letters except for the copies of $x$ and $y$ from $w$, the resulting word is of the form $xyxy\ldots$ (of even or odd length) or $yxyx\ldots$ (of even…
In this thesis we present a semantic representation formalism based on directed graphs and explore its linguistic adequacy and explanatory benefits in the semantics of plurality and quantification. Our graph language covers the essentials…
The study of graph queries in database theory has spanned more than three decades, resulting in a multitude of proposals for graph query languages. These languages differ in the mechanisms. We can identify three main families of languages,…
I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…
A graph is called $k$-representable if there exists a word $w$ over the nodes of the graph, each node occurring exactly $k$ times, such that there is an edge between two nodes $x,y$ if and only after removing all letters distinct from…
A graph G(V, E) is word-representable if there exists a word w over V such that distinct letters x and y alternate in w iff $xy \in E$. We introduce p-complete squares and p-complete square-free word-representable graphs. A word is…
Graphs have a superior ability to represent relational data, like chemical compounds, proteins, and social networks. Hence, graph-level learning, which takes a set of graphs as input, has been applied to many tasks including comparison,…
We investigate three formalisms to specify graph languages, i.e. sets of graphs, based on type graphs. First, we are interested in (pure) type graphs, where the corresponding language consists of all graphs that can be mapped…
Regular word grammars are restricted context-free grammars that define all the recognizable languages of words. This paper generalizes regular grammars from words to certain classes of graphs, by defining regular grammars for unordered…
Graph-based text representation focuses on how text documents are represented as graphs for exploiting dependency information between tokens and documents within a corpus. Despite the increasing interest in graph representation learning,…
Graph learning is a prevalent domain that endeavors to learn the intricate relationships among nodes and the topological structure of graphs. Over the years, graph learning has transcended from graph theory to graph data mining. With the…
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…
Several popular language models represent local contexts in an input text $x$ as bags of words. Such representations are naturally encoded by a sequence graph whose vertices are the distinct words occurring in $x$, with edges representing…
In this paper, we study the word-representability of well-partitioned chordal graphs using split decomposition. We show that every component of the minimal split decomposition of a well-partitioned chordal graph is a split graph. Thus we…