Related papers: A random graph model based on 3-interactions
Pattern counting in graphs is a fundamental primitive for many network analysis tasks, and a number of methods have been developed for scaling subgraph counting to large graphs. Many real-world networks carry a natural notion of strength of…
Random walks constitute a fundamental mechanism for a large set of dynamics taking place on networks. In this article, we study random walks on weighted networks with an arbitrary degree distribution, where the weight of an edge between two…
We study the asymptotic behavior of the maximum degree in the evolving tree model with a choice based on both degree and fitness of a vertex. The tree is constructed in the following recursive way. Each vertex is assigned a parameter to it…
Methods connecting dynamical systems and graph theory have attracted increasing interest in the past few years, with applications ranging from a detailed comparison of different kinds of dynamics to the characterisation of empirical data.…
We study a class models of correlated random networks in which vertices are characterized by \textit{hidden variables} controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological…
Understanding spreading dynamics will benefit society as a whole in better preventing and controlling diseases, as well as facilitating the socially responsible information while depressing destructive rumors. In network-based spreading…
We study the asymptotic properties of distributed consensus algorithms over switching directed random networks. More specifically, we focus on consensus algorithms over independent and identically distributed, directed random graphs, where…
Random intersection graphs containing an underlying community structure are a popular choice for modelling real-world networks. Given the group memberships, the classical random intersection graph is obtained by connecting individuals when…
The structure and dynamic of social network are largely determined by the heterogeneous interaction activity and social capital allocation of individuals. These features interplay in a non-trivial way in the formation of network and…
Random graphs are a central element of the study of complex dynamical networks such as the internet, the brain, or socioeconomic phenomena. New methods to generate random graphs can spawn new applications and give insights into more…
We study a generalisation of the random recursive tree (RRT) model and its multigraph counterpart, the uniform directed acyclic graph (DAG). Here, vertices are equipped with a random vertex-weight representing initial inhomogeneities in the…
Inspired by scientific collaboration networks, especially our empirical analysis of the network of econophysicists, an evolutionary model for weighted networks is proposed. Both degree-driven and weight-driven models are considered.…
We introduce a new random graph model motivated by biological questions relating to speciation. This random graph is defined as the stationary distribution of a Markov chain on the space of graphs on $\{1, \ldots, n\}$. The dynamics of this…
Random graphs with a given degree sequence are often constructed using the configuration model, which yields a random multigraph. We may adjust this multigraph by a sequence of switchings, eventually yielding a simple graph. We show that,…
A general population evolution model is considered. Any individual of the population is characterized by its score. Certain general conditions are assumed concerning the number of the individuals and their scores. Asymptotic theorems are…
Geometric scale-free random graphs are popular models for networks that exhibit as heavy-tailed degree distributions, small-worldness and high clustering. In these models, vertices have weights that cause the heavy-tailed degrees and are…
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…
We consider a class of graph-valued stochastic processes in which each vertex has a type that fluctuates randomly over time. Collectively, the paths of the vertex types up to a given time determine the probabilities that the edges are…
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…
We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of…