Related papers: On the evolution in the configuration model
This paper examines a model involving two dynamic Erd\H{o}s-R\'enyi random graphs that evolve in parallel, with edges in each graph alternating between being present and absent according to specified on- and off-time distributions. A key…
We demonstrate how to generalize two of the most well-known random graph models, the classic random graph, and random graphs with a given degree distribution, by the introduction of hidden variables in the form of extra degrees of freedom,…
We provide algorithms involving edge slides, for a connected simple graph to evolve in a finite number of steps to another connected simple graph in a prescribed configuration, and for the regularization of such a graph by the minimization…
Exponential random graph models (ERGMs) are very flexible for modeling network formation but pose difficult estimation challenges due to their intractable normalizing constant. Existing methods, such as MCMC-MLE, rely on sequential…
The configuration model was originally defined for undirected networks and has recently been extended to directed networks. Many empirical networks are however neither undirected nor completely directed, but instead usually partially…
Exponential Random Graph Models (ERGM) behave peculiar in large networks with thousand(s) of actors (nodes). Standard models containing two-star or triangle counts as statistics are often unstable leading to completely full or empty…
We consider 15 properties of labeled random graphs that are of interest in the graph-theoretical and the graph mining literature, such as clustering coefficients, centrality measures, spectral radius, degree assortativity, treedepth,…
Population structure can be modelled by evolutionary graphs, which can have a substantial, but very subtle influence on the fate of the arising mutants. Individuals are located on the nodes of these graphs, competing with each other to…
We consider the random hypergraph on a finite vertex set by choosing each set of vertices as an hyperedge independently at random. We express the probability distributions of the (lower-)associated simplicial complex and the…
We consider a random geometric hypergraph model based on an underlying bipartite graph. Nodes and hyperedges are sampled uniformly in a domain, and a node is assigned to those hyperedges that lie with a certain radius. From a modelling…
The results of modeling of radiation defects formation and evolution on the surface and in the volume of a crystal are presented in this article. Statistical properties are calculated for the investigated system. It is revealed that defects…
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
We present and investigate an extension of the classical random graph to a general class of inhomogeneous random graph models, where vertices come in different types, and the probability of realizing an edge depends on the types of its…
In this paper we study the component structure of random graphs with independence between the edges. Under mild assumptions, we determine whether there is a giant component, and find its asymptotic size when it exists. We assume that the…
Networks of genetic expression can be modelled by hypergraphs with the additional structure that real coefficients are given to each vertex-edge incidence. The spectra, i.e. the multiset of the eigenvalues, of such hypergraphs, are known to…
Random graphs defined by an occurrence probability that is invariant under node aggregation have been identified recently in the context of network renormalization. The invariance property requires that edges are drawn with a specific…
The edge-degeneracy model is an exponential random graph model that uses the graph degeneracy, a measure of the graph's connection density, and number of edges in a graph as its sufficient statistics. We show this model is relatively…
We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
The aim of this article is to provide space level maps between configuration spaces of graphs that are predicted by algebraic manipulations of cellular chains. More explicitly, we consider edge contraction and half-edge deletion, and…