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Cross-device user matching is a critical problem in numerous domains, including advertising, recommender systems, and cybersecurity. It involves identifying and linking different devices belonging to the same person, utilizing sequence…
A fan is a set of edges with a single common endpoint. A graph is fan-crossing if it admits a drawing in the plane so that each edge is crossed by edges of a fan. It is fan-planar if, in addition, the common endpoint is on the same side of…
Hypergraphs have emerged as a powerful modeling framework to represent systems with multiway interactions, that is systems where interactions may involve an arbitrary number of agents. Here we explore the properties of real-world…
Recently there is huge interest in graph theory and intensive study on computing integer powers of matrices. In this paper, we investigate relationships between one type of graph and well-known Fibonacci sequence. In this content, we…
This paper develops the exact linear relationship between the leading eigenvector of the unnormalized modularity matrix and the eigenvectors of the adjacency matrix. We propose a method for approximating the leading eigenvector of the…
Real-world knowledge can take various forms, including structured, semi-structured, and unstructured data. Among these, knowledge graphs are a form of structured human knowledge that integrate heterogeneous data sources into structured…
An EPG-representation of a graph $G$ is a collection of paths in a plane square grid, each corresponding to a single vertex of $G$, so that two vertices are adjacent if and only if their corresponding paths share infinitely many points. In…
Hypergraphs, as a generalization of simplicial complexes, have long been a subject of interest in their geometric interpretation. The subdivision of simplicial complexes can, to some extent, provide insights into the geometry of simplicial…
The vertices of an interval graph represent intervals over a real line where overlapping intervals denote that their corresponding vertices are adjacent. This implies that the vertices are measurable by a metric and there exists a linear…
It is well known that a graph is bipartite if and only if the spectrum of its adjacency matrix is symmetric. In the present paper, this assertion is dissected into three separate matrix results of wider scope, which are extended also to…
Given a sequence of $r$-uniform hypergraphs $H_n$, denote by $T(H_n)$ the number of monochromatic hyperedges when the vertices of $H_n$ are colored uniformly at random with $c = c_n$ colors. In this paper, we study the joint distribution of…
We study hypergraph visualization via its topological simplification. We explore both vertex simplification and hyperedge simplification of hypergraphs using tools from topological data analysis. In particular, we transform a hypergraph to…
Graphs and hypergraphs combine expressive modeling power with algorithmic efficiency for a wide range of applications. Hedgegraphs generalize hypergraphs further by grouping hyperedges under a color/hedge. This allows hedgegraphs to model…
In this article we discuss a data structure, which combines advantages of two different ways for representing graphs: adjacency matrix and collection of adjacency lists. This data structure can fast add and search edges (advantages of…
We investigate which topological spaces can be constructed as topological realisations of higher-rank graphs. We describe equivalence relations on higher-rank graphs for which the quotient is again a higher-rank graph, and show that…
Graph classification plays an important role is data mining, and various methods have been developed recently for classifying graphs. In this paper, we propose a novel method for graph classification that is based on homotopy equivalence of…
A relational structure is (connected-)homogeneous if every isomorphism between finite (connected) substructures extends to an automorphism of the structure. We investigate notions which generalise (connected-)homogeneity, where…
Context: Edge graphs are graphs whose edges are labelled with identifiers, and nodes can have multiple edges between them. They are used to model a wide range of systems, including networks with distances or degrees of connection and…
Among all uniform hypergraphs with even uniformity, the odd-transversal or odd-bipartite hypergraphs are more close to bipartite simple graphs from the viewpoint of both structure and spectrum. A hypergraph is called minimal…
Face parsing infers a pixel-wise label to each facial component, which has drawn much attention recently. Previous methods have shown their efficiency in face parsing, which however overlook the correlation among different face regions. The…