Related papers: Exploring the 3-Token Graph of Particular Graphs
Real social network datasets provide significant benefits for understanding phenomena such as information diffusion or network evolution. Yet the privacy risks raised from sharing real graph datasets, even when stripped of user identity…
We introduce the concept of a $k$-token signed graph and study some of its combinatorial and algebraic properties. We prove that two switching isomorphic signed graphs have switching isomorphic token graphs. Moreover, we show that the…
Graph invariants provide a powerful analytical tool for investigation of abstract structures of graphs. They, combined in convenient relations, carry global and general information about a graph and its various substructures such as cycle…
We present TikTok StitchGraph: a collection of 36 graphs based on TikTok stitches. With its rapid growth and widespread popularity, TikTok presents a compelling platform for study, yet given its video-first nature the network structure of…
We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size…
The (variational) graph auto-encoder and its variants have been popularly used for representation learning on graph-structured data. While the encoder is often a powerful graph convolutional network, the decoder reconstructs the graph…
Associated to any graph is a toric ideal whose generators record relations among the cuts of the graph. We study these ideals and the geometry of the corresponding toric varieties. Our theorems and conjectures relate the combinatorial…
The problem of characterizing maximal non-Hamiltonian graphs may be naturally extended to characterizing graphs that are maximal with respect to non-traceability and beyond that to $t$-path traceability. We show how traceability behaves…
In the generalized truncation construction, one replaces each vertex of a $k$-regular graph $\Gamma$ with a copy of a graph $\Upsilon$ of order $k$. We investigate the symmetry properties of the graphs constructed in this way, especially in…
Graphlets are defined as k-node connected induced subgraph patterns. For an undirected graph, 3-node graphlets include close triangle and open triangle. When k = 4, there are six types of graphlets, e.g., tailed-triangle and clique are two…
Neural networks are often represented as graphs of connections between neurons. However, despite their wide use, there is currently little understanding of the relationship between the graph structure of the neural network and its…
In this paper we consider the concept of preintersection numbers of a graph. These numbers are determined by the spectrum of the adjacency matrix of the graph, and generalize the intersection numbers of a distance-regular graph. By using…
Let $P$ be a set of $n \geq 5$ points in convex position in the plane. The path graph $G(P)$ of $P$ is an abstract graph whose vertices are non-crossing spanning paths of $P$, such that two paths are adjacent if one can be obtained from the…
Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman \cite{Goodman1949} and Frank \cite{Frank1978}. We revisit a problem formulated by Frank…
This paper introduces provGen, a generator aimed at producing large synthetic provenance graphs with predictable properties and of arbitrary size. Synthetic provenance graphs serve two main purposes. Firstly, they provide a variety of…
The topological (or graph) structures of real-world networks are known to be predictive of multiple dynamic properties of the networks. Conventionally, a graph structure is represented using an adjacency matrix or a set of hand-crafted…
Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph…
In this paper we resolve the complexity of the isomorphism problem on all but finitely many of the graph classes characterized by two forbidden induced subgraphs. To this end we develop new techniques applicable for the structural and…
In this paper, new graphs $G_\tau=\left(V,E\right)$ are constructed from the discrete topological space $(X,\tau)\ $ . Several properties of this type of graphs are given such that: the clique number equals the number of elements in X also…
A graph is a mathematical object consisting of a set of vertices and a set of edges connecting vertices. Graphs can be drawn on paper in various ways, but until recently all published methods of drawing graphs have had undesirable…