Related papers: Random networks with sublinear preferential attach…
Preferential attachment is an appealing edge generating mechanism for modeling social networks. It provides both an intuitive description of network growth and an explanation for the observed power laws in degree distributions. However,…
We consider models of evolving networks $\{\mathcal{G}_n:n\geq 0\}$ modulated by two parameters: an attachment function $f:\mathbb{N}_0\to\mathbb{R}_+$ and a (possibly random) attachment sequence $\{m_i:i\geq 1\}$. Starting with a single…
Network models with preferential attachment, where new nodes are injected into the network and form links with existing nodes proportional to their current connectivity, have been well studied for some time. Extensions have been introduced…
We introduce a random graph model based on k-trees, which can be generated by applying a probabilistic preferential attachment rule, but which also has a simple combinatorial description. We carry out a precise distributional analysis of…
We propose a new mechanism leading to scale-free networks which is based on the presence of an intrinsic character of a vertex called fitness. In our model, a vertex $i$ is assigned a fitness $x_i$, drawn from a given probability…
We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…
We present a simple model of network growth and solve it by writing down the dynamic equations for its macroscopic characteristics like the degree distribution and degree correlations. This allows us to study carefully the percolation…
The preferential attachment network with fitness is a dynamic random graph model. New vertices are introduced consecutively and a new vertex is attached to an old vertex with probability proportional to the degree of the old one multiplied…
We investigate the growth of connectivity in a network. In our model, starting with a set of disjoint nodes, links are added sequentially. Each link connects two nodes, and the connection rate governing this random process is proportional…
We consider the problem of selecting important nodes in a random network, where the nodes connect to each other randomly with certain transition probabilities. The node importance is characterized by the stationary probabilities of the…
In this paper we focus on the problem of the degree sequence for the following random graph process. At any time-step $t$, one of the following three substeps is executed: with probability $\alpha_1$, a new vertex $x_t$ and $m$ edges…
We investigate choice-driven network growth. In this model, nodes are added one by one according to the following procedure: for each addition event a set of target nodes is selected, each according to linear preferential attachment, and a…
Discriminating between competing explanatory models as to which is more likely responsible for the growth of a network is a problem of fundamental importance for network science. The rules governing this growth are attributed to mechanisms…
Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This…
Percolation, the formation of a macroscopic connected component, is a key feature in the description of complex networks. The dynamical properties of a variety of systems can be understood in terms of percolation, including the robustness…
We study the appearance of the giant component in random subgraphs of a given large finite graph G=(V,E) in which each edge is present independently with probability p. We show that if G is an expander with vertices of bounded degree, then…
This is the first of two papers about the structure of Kauffman networks. In this paper we define the relevant elements of random networks of automata, following previous work by Flyvbjerg and Flyvbjerg and Kjaer, and we study numerically…
We describe the complex global structure of giant components in directed multiplex networks which generalizes the well-known bow-tie structure, generic for ordinary directed networks. By definition, a directed multiplex network contains…
There are diverse mechanisms driving the evolution of social networks. A key open question dealing with understanding their evolution is: How various preferential linking mechanisms produce networks with different features? In this paper we…
Centrality measures aim to indicate who is important in a network. Various notions of `being important' give rise to different centrality measures. In this paper, we study how important the central vertices are for the connectivity…