Related papers: Generalized Word-Representable Graphs
Recent progress in language modeling has expanded the range of tasks that can be approached through natural language interfaces, including problems that require structured reasoning. However, it remains unclear how effectively…
A graph $G=(V,E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $w$ if and only if $(x,y)\in E$. A triangular grid graph is a subgraph of a tiling of the plane with…
Many models learn representations of knowledge graph data by exploiting its low-rank latent structure, encoding known relations between entities and enabling unknown facts to be inferred. To predict whether a relation holds between…
In many ways, graphs are the main modality of data we receive from nature. This is due to the fact that most of the patterns we see, both in natural and artificial systems, are elegantly representable using the language of graph structures.…
A word-graph Gw is a digraph represented by a word w such that the vertex-set V(Gw) is the alphabet of w and the edge-set E(Gw) is determined by non-identical adjacent letter pairs in w. In this paper we study the strong-connectivity of…
Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…
Graph Convolutional Networks (GCNs) have shown strong performance in learning text representations for various tasks such as text classification, due to its expressive power in modeling graph structure data (e.g., a literature citation…
Traditionally, graph algorithms get a single graph as input, and then they should decide if this graph satisfies a certain property $\Phi$. What happens if this question is modified in a way that we get a possibly infinite family of graphs…
Graph is a universe data structure that is widely used to organize data in real-world. Various real-word networks like the transportation network, social and academic network can be represented by graphs. Recent years have witnessed the…
In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…
In this short note, we first associate a new simple undirected graph with a given word over an ordered alphabet of $n$-letters. We will call it the Lyndon graph of that word. Then, we introduce the concept of the Lyndon-word representable…
Jones et al. (2015) introduced the notion of $u$-representable graphs, where $u$ is a word over $\{1, 2\}$ different from $22\cdots2$, as a generalization of word-representable graphs. Kitaev (2016) showed that if $u$ is of length at least…
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…
Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…
Recent years have witnessed rapid advances in graph representation learning, with the continuous embedding approach emerging as the dominant paradigm. However, such methods encounter issues regarding parameter efficiency, interpretability,…
The class of Parikh word representable graphs were recently introduced. In this work, we further develop its general theory beyond the binary alphabet. Our main result shows that this class is equivalent to the class of bipartite…
A 1-11-representation of a graph $G(V,E)$ is a word over the alphabet $V$ such that two distinct vertices $x$ and $y$ are adjacent if and only if the restricted word $w{x,y}$ (obtained from $w$ by deleting all letters except $x$ and $y$)…
A graph $G = (V, E)$ is word-representable, if there exists a word w over the alphabet V such that for letters ${x, y} \in V$ , $x$ and $y$ alternate in $w$ if and only if $xy \in E$. In this paper, we prove that any non-empty…
Once the set of finite graphs is equipped with an algebra structure (arising from the definition of operations that generalize the concatenation of words), one can define the notion of a recognizable set of graphs in terms of finite…
The representation number of a graph is the minimum number of copies of each vertex required to represent the graph as a word, such that the letters corresponding to vertices $x$ and $y$ alternate if and only if $xy$ is an edge in the…