Related papers: Term Graph Representations for Cyclic Lambda-Terms
Graph-based collaborative filtering is capable of capturing the essential and abundant collaborative signals from the high-order interactions, and thus received increasingly research interests. Conventionally, the embeddings of users and…
Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order…
Temporal graphs are commonly used to represent time-resolved relations between entities in many natural and artificial systems. Many techniques were devised to investigate the evolution of temporal graphs by comparing their state at…
Many topological data analysis (TDA) pipelines compute large collections of persistence diagrams, yet vectorizations and kernel methods discard the rank-induced implication relations among persistence intervals that are essential for…
The spectral properties of traditional (dyadic) graphs, where an edge connects exactly two vertices, are widely studied in different applications. These spectral properties are closely connected to the structural properties of dyadic…
Graph is an important data representation which appears in a wide diversity of real-world scenarios. Effective graph analytics provides users a deeper understanding of what is behind the data, and thus can benefit a lot of useful…
A few steps are made towards representation theory of embeddability among uncountable graphs. A monotone class of graphs is defined by forbidding countable subgraphs, related to the graph's end-structure. Using a combinatorial theorem of…
As an efficient model for knowledge organization, the knowledge graph has been widely adopted in several fields, e.g., biomedicine, sociology, and education. And there is a steady trend of learning embedding representations of knowledge…
Graphs are a representation of structured data that captures the relationships between sets of objects. With the ubiquity of available network data, there is increasing industrial and academic need to quickly analyze graphs with billions of…
Word-representable graphs, characterized by the existence of a semi-transitive orientation, form a well-studied class of graphs. Comparability graphs form another well-studied class and constitute a subclass of word-representable graphs.…
The main goal of this note is to provide a First-Order Logic with Betweenness (FOLB) axiomatization of the main classes of graphs occurring in Metric Graph Theory, in analogy to Tarski's axiomatization of Euclidean geometry. We provide such…
Graphs, such as social networks, word co-occurrence networks, and communication networks, occur naturally in various real-world applications. Analyzing them yields insight into the structure of society, language, and different patterns of…
In this work, we study the utility of graph embeddings to generate latent user representations for trust-based collaborative filtering. In a cold-start setting, on three publicly available datasets, we evaluate approaches from four method…
Word-representable graphs are a subset of graphs that may be represented by a word $w$ over an alphabet composed of the vertices in the graph. In such graphs, an edge exists if and only if the occurrences of the corresponding vertices…
The $\lambda$-calculus is a handy formalism to specify the evaluation of higher-order programs. It is not very handy, however, when one interprets the specification as an execution mechanism, because terms can grow exponentially with the…
We study the hairy graph homology of a cyclic operad; in particular we show how to assemble corresponding hairy graph cohomology classes to form cocycles for ordinary graph homology, as defined by Kontsevich. We identify the part of hairy…
The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction ,…
Human knowledge provides a formal understanding of the world. Knowledge graphs that represent structural relations between entities have become an increasingly popular research direction towards cognition and human-level intelligence. In…
End-periodic homotopy equivalences of infinite, locally finite graphs serve as dimension-one analogs of the end-periodic automorphisms traditionally defined on infinite-type surfaces. We demonstrate that if $\Gamma$ is an infinite graph…
We deal with first-order definability in the embeddability ordering $( \mathcal{D}; \leq)$ of finite directed graphs. A directed graph $G\in \mathcal{D}$ is said to be embeddable into $G' \in \mathcal{D}$ if there exists an injective graph…