Related papers: Layered Graph Drawing with Few Gaps and Few Crossi…
The entities in directed networks arising from real-world interactions are often naturally organized under some hierarchical structure. Given a directed, weighted, graph with edges and node labels, we introduce ranking problem where the…
Given an undirected graph G, the edge orientation problem asks for assigning a direction to each edge to convert G into a directed graph. The aim is to minimize the maximum out degree of a vertex in the resulting directed graph. This…
Listing triangles is a fundamental graph problem with many applications, and large graphs require fast algorithms. Vertex ordering allows the orientation of edges from lower to higher vertex indices, and state-of-the-art triangle listing…
Given a set D of nonnegative integers, we derive the asymptotic number of graphs with a givenvnumber of vertices, edges, and such that the degree of every vertex is in D. This generalizes existing results, such as the enumeration of graphs…
Graphs face challenges when dealing with massive datasets. They are essential tools for modeling interconnected data and often become computationally expensive. Graph embedding techniques, on the other hand, provide an efficient approach.…
Graph labellings have been a very fruitful area of research in the last four decades. However, despite the staggering number of papers published in the field (over 1000), few general results are available, and most papers deal with…
Graph signal processing (GSP) provides a powerful framework for analyzing signals arising in a variety of domains. In many applications of GSP, multiple network structures are available, each of which captures different aspects of the same…
Hypergraphs are a useful abstraction for modeling multiway relationships in data, and hypergraph clustering is the task of detecting groups of closely related nodes in such data. Graph clustering has been studied extensively, and there are…
Hive plots are a graph visualization style placing vertices on a set of radial axes emanating from a common center and drawing edges as smooth curves connecting their respective endpoints. In previous work on hive plots, assignment to an…
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…
The k-planar graphs, which are (usually with small values of k such as 1, 2, 3) subject to recent intense research, admit a drawing in which edges are allowed to cross, but each one edge is allowed to carry at most k crossings. In recently…
In the graph stream model of computation, an algorithm processes the edges of an input graph in one or more sequential passes while using a memory sublinear in the input size. This model poses significant challenges for constructing long…
Graph embedding methods embed the nodes in a graph in low dimensional vector space while preserving graph topology to carry out the downstream tasks such as link prediction, node recommendation and clustering. These tasks depend on a…
This paper considers structures of systems beyond dyadic (pairwise) interactions and investigates mathematical modeling of multi-way interactions and connections as hypergraphs, where captured relationships among system entities are…
Complex systems of interacting components often can be modeled by a simple graph $\mathcal{G}$ that consists of a set of $n$ nodes and a set of $m$ edges. Such a graph can be represented by an adjacency matrix $A\in\R^{n\times n}$, whose…
A good edge-labelling of a simple, finite graph is a labelling of its edges with real numbers such that, for every ordered pair of vertices (u,v), there is at most one nondecreasing path from u to v. In this paper we prove that any graph on…
Interactions in many real-world phenomena can be explained by a strong hierarchical structure. Typically, this structure or ranking is not known; instead we only have observed outcomes of the interactions, and the goal is to infer the…
Graphs, consisting of vertices and edges, are vital for representing complex relationships in fields like social networks, finance, and blockchain. Visualizing these graphs helps analysts identify structural patterns, with readability…
Multilayer graphs are appealing mathematical tools for modeling multiple types of relationship in the data. In this paper, we aim at analyzing multilayer graphs by properly combining the information provided by individual layers, while…
Beyond-planarity focuses on the study of geometric and topological graphs that are in some sense nearly-planar. Here, planarity is relaxed by allowing edge crossings, but only with respect to some local forbidden crossing configurations.…