Related papers: Wheel Random Apollonian Graphs
Given a symmetric $n\times n$ matrix $P$ with $0 \le P(u, v)\le 1$, we define a random graph $G_{n, P}$ on $[n]$ by independently including any edge $\{u, v\}$ with probability $P(u, v)$. For $k\ge 1$ let $\mathcal{A}_k$ be the property of…
Real social networks are often compared to random graphs in order to assess whether their typological structure could be the result of random processes. However, an Erd\H{o}s-R\'enyi random graph in large scale is often lack of local…
We describe a simple algorithm based on a Markov chain process to generate simply connected acyclic directed graphs over a fixed set of vertices. This algorithm is an extension of a previous one, designed to generate acyclic digraphs, non…
Graphs are useful structures that can model several important real-world problems. Recently, learning graphs have drawn considerable attention, leading to the proposal of new methods for learning these data structures. One of these studies…
A wheel graph consists of a cycle along with a center vertex connected to every vertex in the cycle. In this paper we show that every subgraph of a wheel graph has list coupled chromatic number at most 5, and this coloring can be found in…
We introduce ring theoretic constructions that are similar to the construction of wreath product of groups. In particular, for a given graph $\Gamma=(V,E)$ and an associate algebra $A,$ we construct an algebra $B=A\, wr\, L(\Gamma)$ with…
The hyperbolic random graph model (HRG) has proven useful in the analysis of scale-free networks, which are ubiquitous in many fields, from social network analysis to biology. However, working with this model is algorithmically and…
The paper provides the first constructions of strongly regular graphs and association schemes from weakly regular plateaued functions over finite fields of odd characteristic. We generalize the construction method of strongly regular graphs…
In this letter, we propose a simple rule that generates scale-free networks with very large clustering coefficient and very small average distance. These networks are called {\bf Random Apollonian Networks}(RANs) as they can be considered…
We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…
We introduce the P\'olya threshold graph model and derive its stochastic and algebraic properties. This random threshold graph is generated sequentially via a two-color P\'olya urn process. Starting from an empty graph, each time step…
We study directed random graphs (random graphs whose edges are directed), and present new results on the so-called strong components of those graphs. We provide analytic and simulation results on two special classes of strong component,…
Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have…
The definition of edge-regularity in graphs is a relaxation of the definition of strong regularity, so strongly regular graphs are edge-regular and, not surprisingly, the family of edge-regular graphs is much larger and more diverse than…
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…
We introduce a new family of networks, the Apollonian networks, that are simultaneously scale-free, small world, Euclidean, space-filling and matching graphs. These networks have a wide range of applications ranging from the description of…
It has been an open problem to find the Moore-Penrose inverses of the incidence, Laplacian, and signless Laplacian matrices of families of graphs except trees and unicyclic graphs. Since the inverse formulas for an odd unicyclic graph and…
Graph neural networks have become a staple in problems addressing learning and analysis of data defined over graphs. However, several results suggest an inherent difficulty in extracting better performance by increasing the number of…
The chordal ring (CR) graphs are a well-known family of graphs used to model some interconnection networks for computer systems in which all nodes are in a cycle. Generalizing the CR graphs, in this paper, we introduce the families of…
Inspired by the prospect of having discretized spaces emerge from random graphs, we construct a collection of simple and explicit exponential random graph models that enjoy, in an appropriate parameter regime, a roughly constant vertex…