Related papers: Characterizing and Recognizing Twistedness
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
In one complex variable, the cross ratio is a well-known quantity associated with four given points in the complex plane that remains invariant under linear fractional maps. In particular, if one knows where three points in the complex…
Say that an edge of a graph G dominates itself and every other edge adjacent to it. An edge dominating set of a graph G = (V,E) is a subset of edges E' of E which dominates all edges of G. In particular, if every edge of G is dominated by…
We show that any connected regular graph with $d+1$ distinct eigenvalues and odd-girth $2d+1$ is distance-regular, and in particular that it is a generalized odd graph.
We study a question that lies at the intersection of classical research subjects in Topological Graph Theory and Graph Drawing: Computing a drawing of a graph with a prescribed number of crossings on a given set $S$ of points, while…
In a group, a non-trivial element is called a generalized torsion element if some non-empty finite product of its conjugates equals to the identity. We say that a knot has generalized torsion if its knot group admits such an element. For a…
It is well established that a general pair of twisted cubic curves in complex projective space has ten common secant lines. As an initial investigation, we show that the monodromy group of the ten common secant lines over the complex…
The Friendship Paradox is a simple and powerful statement about node degrees in a graph (Feld 1991). However, it only applies to undirected graphs with no edge weights, and the only node characteristic it concerns is degree. Since many…
Random graphs with latent geometric structure are popular models of social and biological networks, with applications ranging from network user profiling to circuit design. These graphs are also of purely theoretical interest within…
We present Twisted Edges, a unified framework for designing Linked Knot (LK) structures using labeled non-manifold surface meshes. While the concept of edge twists, originating in topological graph theory, is foundational to these designs,…
The basic (and traditional) crossing number problem is to determine the minimum number of crossings in a topological drawing of an input graph in the plane. We develop a unified framework yielding fixed-parameter tractable (FPT) algorithms…
After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…
We consider an edge-weighted uniform random graph with a given degree sequence (Repeated Configuration Model) which is a useful approximation for many real-world networks. It has been observed that the vertices which are separated from the…
Given a causal graph representing the data-generating process shared across different domains/distributions, enforcing sufficient graph-implied conditional independencies can identify domain-general (non-spurious) feature representations.…
The vertices of a finite state system are usually a subset of the natural numbers. Most algorithms relative to these systems only use this fact to select vertices. For infinite state systems, however, the situation is different: in…
This contribution proposes a new approach towards developing a class of probabilistic methods for classifying attributed graphs. The key concept is random attributed graph, which is defined as an attributed graph whose nodes and edges are…
Frequently, knots are enumerated by their crossing number. However, the number of knots with crossing number $c$ grows exponentially with $c$, and to date computer-assisted proofs can only classify diagrams up to around twenty crossings.…
The visual complexity of a graph drawing is defined as the number of 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 draw two collinear…
For a drawing of a labeled graph, the rotation of a vertex or crossing is the cyclic order of its incident edges, represented by the labels of their other endpoints. The extended rotation system (ERS) of the drawing is the collection of the…
The paper uses statistical and differential geometric motivation to acquire prior information about the learning capability of an artificial neural network on a given dataset. The paper considers a broad class of neural networks with…