Related papers: A dynamic network in a dynamic population: asympto…
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,…
This paper proposes a stochastic block model with dynamics where the population grows using preferential attachment. Nodes with higher weighted degree are more likely to recruit new nodes, and nodes always recruit nodes from their own…
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…
In this paper, we investigate the asymptotic behavior of individual-based models describing the evolution of a population structured by a real trait, subject to selection and mutation. We consider two different sets of assumptions: first,…
Many real-world social networks constantly change their global properties over time, such as the number of edges, size and density. While temporal and local properties of social networks have been extensively studied, the origin of their…
This work concerns a many-body deterministic model that displays life-like properties as emergence, complexity, self-organization, spontaneous compartmentalization, and self-regulation. The model portraits the dynamics of an ensemble of…
We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the…
We introduce a growing network evolution model with nodal attributes. The model describes the interactions between potentially violent V and non-violent N agents who have different affinities in establishing connections within their own…
We consider a dynamic social network model in which agents play repeated games in pairings determined by a stochastically evolving social network. Individual agents begin to interact at random, with the interactions modeled as games. The…
In the stochastic network model of Britton and Lindholm [Dynamic random networks in dynamic populations. Journal of Statistical Physics, 2010], the number of individuals evolves according to a supercritical linear birth and death process,…
We generalize the poissonian evolving random graph model of Bauer and Bernard to deal with arbitrary degree distributions. The motivation comes from biological networks, which are well-known to exhibit non poissonian degree distribution. A…
We introduce a new oriented evolving graph model inspired by biological networks. A node is added at each time step and is connected to the rest of the graph by random oriented edges emerging from older nodes. This leads to a statistical…
We study structural properties of growing networks where both addition and deletion of nodes are possible. Our model network evolves via two independent processes. With rate r, a node is added to the system and this node links to a randomly…
Using a simple model with link removals as well as link additions, we show that an evolving network is scale free with a degree exponent in the range of (2, 4]. We then establish a relation between the network evolution and a set of…
Researchers have devoted themselves to exploring static features of social networks and further discovered many representative characteristics, such as power law in the degree distribution and assortative value used to differentiate social…
Traditional mathematical models of epidemic disease had for decades conventionally considered static structure for contacts. Recently, an upsurge of theoretical inquiry has strived towards rendering the models more realistic by…
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…
We consider the population dynamics of a set of species whose network of catalytic interactions is described by a directed graph. The relationship between the attractors of this dynamics and the underlying graph theoretic structures like…
A dynamic model of a society is studied where each person is an uncorrelated and non-interacting random walker. A dynamical random graph represents the acquaintance network of the society whose nodes are the individuals and links are the…
In this study we introduce and analyze the statistical structural properties of a model of growing networks which may be relevant to social networks. At each step a new node is added which selects 'k' possible partners from the existing…