Related papers: Symbolic Dynamics Generated by a Combination of Gr…
$\omega$-periodic graphs are introduced and studied. These are graphs which arise as the limits of periodic extensions of the nearest neighbor graph on the integers. We observe that all bounded degree $\omega$-periodic graphs are ameanable.…
We use symbolic dynamics to study discrete-time dynamical systems with multiple time delays. We exploit the concept of avoiding sets, which arise from specific non-generating partitions of the phase space and restrict the occurrence of…
How do real graphs evolve over time? What are ``normal'' growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large…
A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…
Population structure affects the outcome of natural selection. Static population structures can be described by graphs, where individuals occupy the nodes, and interactions occur along the edges. General conditions for evolutionary success…
We discuss a link between graph theory and geometry that arises when considering graph dynamical systems with odd interactions. The equilibrium set in such systems is not a collection of isolated points, but rather a union of manifolds,…
A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…
For networks of coupled dynamical systems we characterize admissible functions, that is, functions whose gradient is an admissible vector field. The schematic representation of a gradient network dynamical system is of an undirected cell…
An example of a discrete pregeometry on a microscopic scale is introduced. The model is a directed dyadic acyclic graph. This is the particular case of a causal set. The particles in this model must be self-organized repetitive structures.…
A graph is path-pairable if for any pairing of its vertices there exist edge disjoint paths joining the vertices in each pair. We obtain sharp bounds on the maximum possible diameter of path-pairable graphs which either have a given number…
We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs…
We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement…
A graphical model provides a compact and efficient representation of the association structure of a multivariate distribution by means of a graph. Relevant features of the distribution are represented by vertices, edges and other…
Consider a family $\mathcal{T}$ of 3-connected graphs of moderate growth, and let $\mathcal{G}$ be the class of graphs whose 3-connected components are graphs in $\mathcal{T}$. We present a general framework for analyzing such graphs…
Many growing networks possess accelerating statistics where the number of links added with each new node is an increasing function of network size so the total number of links increases faster than linearly with network size. In particular,…
Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…
Structural properties of evolving random graphs are investigated. Treating linking as a dynamic aggregation process, rate equations for the distribution of node to node distances (paths) and of cycles are formulated and solved analytically.…
This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…
Sequences of correlated binary patterns can represent many time-series data including text, movies, and biological signals. These patterns may be described by weighted combinations of a few dominant structures that underpin specific…
We consider random temporal graphs, a version of the classical Erd\H{o}s--R\'enyi random graph G(n,p) where additionally, each edge has a distinct random time stamp, and connectivity is constrained to sequences of edges with increasing time…