Related papers: Drawing Order Diagrams Through Two-Dimension Exten…
In this paper, we use theory of rough set to study graphs using the concept of orbits. We investigate the indiscernibility partitions and approximations of graphs induced by orbits of graphs. We also study rough membership functions,…
We propose a new approach to text semantic analysis and general corpus analysis using, as termed in this article, a "bi-gram graph" representation of a corpus. The different attributes derived from graph theory are measured and analyzed as…
In this paper we present a new approach to visualize directed graphs and their hierarchies that completely departs from the classical four-phase framework of Sugiyama and computes readable hierarchical visualizations that contain the…
String diagrams are an increasingly popular algebraic language for the analysis of graphical models of computations across different research fields. Whereas string diagrams have been thoroughly studied as semantic structures, much less…
The paper is devoted to developing subdifferential theory for set-valued mappings taking values in ordered infinite-dimensional spaces. This study is motivated by applications to problems of vector and set optimization with various…
Depending on the node ordering, an adjacency matrix can highlight distinct characteristics of a graph. Deriving a "proper" node ordering is thus a critical step in visualizing a graph as an adjacency matrix. Users often try multiple matrix…
Edge casing is a well-known method to improve the readability of drawings of non-planar graphs. A cased drawing orders the edges of each edge crossing and interrupts the lower edge in an appropriate neighborhood of the crossing. Certain…
This book dwells on mathematical and algorithmic issues of data analysis based on generality order of descriptions and respective precision. To speak of these topics correctly, we have to go some way getting acquainted with the important…
The quest for efficient sorting is ongoing, and we will explore a graph-based stable sorting strategy, in particular employing comparison graphs. We use the topological sort to map the comparison graph to a linear domain, and we can…
Conditional graph generation tasks involve training a model to generate a graph given a set of input conditions. Many previous studies employ autoregressive models to incrementally generate graph components such as nodes and edges. However,…
While orthogonal drawings have a long history, smooth orthogonal drawings have been introduced only recently. So far, only planar drawings or drawings with an arbitrary number of crossings per edge have been studied. Recently, a lot of…
We report on the phase transition of finding a complete subgraph, of specified dimensions, in a bipartite graph. Finding a complete subgraph in a bipartite graph is a problem that has growing attention in several domains, including…
Force-directed algorithms are among the most flexible methods for calculating layouts of simple undirected graphs. Also known as spring embedders, such algorithms calculate the layout of a graph using only information contained within the…
We study set systems formed by neighborhoods in graphs of bounded twin-width. We start by proving that such graphs have linear neighborhood complexity, in analogy to previous results concerning graphs from classes with bounded expansion and…
Two algorithms are presented for "compiling" influence diagrams into a set of simple decision rules. These decision rules define simple-to-execute, complete, consistent, and near-optimal decision procedures. These compilation algorithms can…
This paper discusses the formalization of proofs "by diagram chasing", a standard technique for proving properties in abelian categories. We discuss how the essence of diagram chases can be captured by a simple many-sorted first-order…
We define the \emph{visual complexity} of a plane graph drawing to be the number of basic geometric objects needed to represent all its edges. In particular, one object may represent multiple edges (e.g., one needs only one line segment to…
String diagrams are a graphical language used to represent processes that can be composed sequentially or in parallel, which correspond graphically to horizontal or vertical juxtaposition. In this paper we demonstrate how to compute the…
As networks and their structure have become a major field of research, a strong demand for network visualization has emerged. We address this challenge by formalizing the well established spring layout in terms of dynamic equations. We thus…
An ordered binary decision diagram (OBDD) is a directed acyclic graph that represents a Boolean function. OBDDs are also known as special cases of oblivious read-once branching programs in the field of complexity theory. Since OBDDs have…