Related papers: Carrying capacity in growing networks
Unlike the well-studied models of growing networks, where the dominant dynamics consist of insertions of new nodes and connections, and rewiring of existing links, we study {\em ad hoc} networks, where one also has to contend with rapid and…
We compute the stationary in-degree probability, $P_{in}(k)$, for a growing network model with directed edges and arbitrary out-degree probability. In particular, under preferential linking, we find that if the nodes have a light tail…
The availability of large scale streaming network data has reinforced the ubiquity of power-law distributions in observations and enabled precision measurements of the distribution parameters. The increased accuracy of these measurements…
Most of the networks observed in real life obey power-law degree distribution. It is hypothesized that the emergence of such a degree distribution is due to preferential attachment of the nodes. Barabasi-Albert model is a generative…
Recent years have seen a large amount of interest in epidemics on networks as a way of representing the complex structure of contacts capable of spreading infections through the modern human population. The configuration model is a popular…
We study the dynamical properties of a finite dynamical network composed of two interacting populations, namely; extrovert ($a$) and introvert ($b$). In our model, each group is characterized by its size ($N_a$ and $N_b$) and preferred…
In the study of complex networks almost all theoretical models have the property of infinite growth, but the size of actual networks is finite. According to statistics from the China Internet IPv4 (Internet Protocol version 4) addresses,…
In this paper we present a generalized model for network growth that links the microscopical agent strategies with the large scale behavior. This model is intended to reproduce the largest number of features of the Internet network at the…
We consider an SIR epidemic model propagating on a configuration model network, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemic is summed up into three…
We analyze dynamic random network models where younger vertices connect to older ones with probabilities proportional to their degrees as well as a propensity kernel governed by their attribute types. Using stochastic approximation…
A non-local model describing the growth of a tree-like transportation network with given allocation rules is proposed. In this model we focus on tree like networks, and the network transports the very resource it needs to build itself. Some…
The directed preferential attachment model is revisited. A new exact characterization of the limiting in- and out-degree distribution is given by two \emph{independent} pure birth processes that are observed at a common exponentially…
We investigate the growth of a class of networks in which a new node first picks a mediator at random and connects with $m$ randomly chosen neighbors of the mediator at each time step. We show that degree distribution in such a…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
Real networks often grow through the sequential addition of new nodes that connect to older ones in the graph. However, many real systems evolve through the branching of fundamental units, whether those be scientific fields, countries, or…
The microscopic and macroscopic dynamics of random networks is investigated in the strong-dilution limit (i.e. for sparse networks). By simulating chaotic maps, Stuart-Landau oscillators, and leaky integrate-and-fire neurons, we show that a…
We present a generator of random networks where both the degree-dependent clustering coefficient and the degree distribution are tunable. Following the same philosophy as in the configuration model, the degree distribution and the…
We study collaboration networks in terms of evolving, self-organizing bipartite graph models. We propose a model of a growing network, which combines preferential edge attachment with the bipartite structure, generic for collaboration…
We analyze the spreading of viruses in scale-free networks with high clustering and degree correlations, as found in the Internet graph. For the Suscetible-Infected-Susceptible model of epidemics the prevalence undergoes a phase transition…
A random network is grown by introducing at unit rate randomly selected nodes on the Euclidean space. A node is randomly connected to its $i$-th predecessor of degree $k_i$ with a directed link of length $\ell$ using a probability…