Related papers: Estimating Graph Dynamics from Population Observat…
In this paper we consider a dynamic version of the Chung-Lu random graph in which the edges alternate between being present and absent. The main contribution concerns a technique by which one can estimate the underlying dynamics from…
This paper introduces graphemes for constructing and analyzing stochastic processes that describe the evolution of large dynamic graphs. Unlike graphons, which capture the static properties of dense graphs via exchangeability or subgraph…
We analyze evolutionary dynamics on graphs, where the nodes represent individuals of a population. The links of a node describe which other individuals can be displaced by the offspring of the individual on that node. Amplifiers of…
Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…
We explore the voter model dynamics on a directed random graph model ensemble (digraphs), given by the Directed Configuration Model. The voter model captures the evolution of opinions over time on a graph where each vertex represents an…
We consider a dynamic Erd\H{o}s-R\'enyi random graph (ERRG) on $n$ vertices in which each edge switches on at rate $\lambda$ and switches off at rate $\mu$, independently of other edges. The focus is on the analysis of the evolution of the…
We consider a number $\nu_n$ of components in a random graph $G(n,p)$ with $n$ vertices, where the probability of an edge is equal to $p$. By operating with special generating functions we shows the next asymptotic relation for factorial…
Evolutionary graph theory (EGT) studies the effect of population structure on evolutionary dynamics. The vertices of the graph represent the $N$ individuals. The edges denote interactions for competitive replacement. Two standard update…
Consider a graph whose vertices are populated by identical objects, together with an algorithm for the time-evolution of the number of objects placed at each of the vertices. The discrete dynamics of these objects can be observed and…
We study the intersection of a random geometric graph with an Erd\H{o}s-R\'enyi graph. Specifically, we generate the random geometric graph $G(n, r)$ by choosing $n$ points uniformly at random from $D=[0, 1]^2$ and joining any two points…
The Moran process, as studied by [Lieberman, E., Hauert, C. and Nowak, M. Evolutionary dynamics on graphs. Nature 433, pp. 312-316 (2005)], is a stochastic process modeling the spread of genetic mutations in populations. In this process,…
We investigate a randomly evolving process of subgraphs in an underlying host graph using the spectral theory of semigroups related to the Tsetlin library and hyperplane arrangements. Starting with some initial subgraph, at each iteration,…
Evolutionary graph theory studies the evolutionary dynamics in a population structure given as a connected graph. Each node of the graph represents an individual of the population, and edges determine how offspring are placed. We consider…
We deal with a random graph model where at each step, a vertex is chosen uniformly at random, and it is either duplicated or its edges are deleted. Duplication has a given probability. We analyse the limit distribution of the degree of a…
We define a general model of stochastically-evolving graphs, namely the \emph{Edge-Uniform Stochastically-Evolving Graphs}. In this model, each possible edge of an underlying general static graph evolves independently being either alive or…
We consider random graphs in which the edges are allowed to be dependent. In our model the edge dependence is quite general, we call it $p$-robust random graph. It means that every edge is present with probability at least $p$, regardless…
A random walk is a basic stochastic process on graphs and a key primitive in the design of distributed algorithms. One of the most important features of random walks is that, under mild conditions, they converge to a stationary distribution…
We investigate the dynamic formation of regular random graphs. In our model, we pick a pair of nodes at random and connect them with a link if both of their degrees are smaller than d. Starting with a set of isolated nodes, we repeat this…
We introduce a model for a growing random graph based on simultaneous reproduction of the vertices. The model can be thought of as a generalisation of the reproducing graphs of Southwell and Cannings and Bonato et al to allow for a random…
We consider the median dynamics process in general graphs. In this model, each vertex has an independent initial opinion uniformly distributed in the interval [0,1] and, with rate one, updates its opinion to coincide with the median of its…