Related papers: Kinetics of node splitting in evolving complex net…
A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…
We consider a preferential attachment model that incorporates an anomaly. Our goal is to understand the evolution of the network before and after the occurrence of the anomaly by studying the influence of the anomaly on the structural…
In this paper, we present a simple model of scale-free networks that incorporates both preferential & random attachment and anti-preferential & random deletion at each time step. We derive the degree distribution analytically and show that…
We show that not only preferential attachment but also preferential depletion leads to scale-free networks. The resulting degree distribution exponents is typically less than two (5/3) as opposed to the case of the growth models studied…
Preferential attachment is a popular generative mechanism to explain the widespread observation of power law distributed networks. We introduce an alternative explanation for the phenomenon by allowing the link growth rates to vary across…
In this paper, we first discuss the origin of preferential attachment. Then we establish the generalized preferential attachment which has two new properties; first, it encapsulates both the topological and weight aspects of a network,…
Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of…
In a recent work \cite{LiuJoladSchZia13}, we introduced dynamic networks with preferred degrees and presented simulation and analytic studies of a single, homogeneous system as well as two interacting networks. Here, we extend these studies…
Growing attention has been brought to the fact that many real directed networks exhibit hierarchy and directionality as measured through techniques like Trophic Analysis and non-normality. We propose a simple growing network model where the…
In this article we presented a brief study of the main network models with growth and preferential attachment. Such models are interesting because they present several characteristics of real systems. We started with the classical model…
We highlight intriguing features of complex networks that are grown by \emph{redirection}. In this mechanism, a target node is chosen uniformly at random from the pre-existing network nodes and the new node attaches either to this initial…
The linear preferential attachment hypothesis has been shown to be quite successful to explain the existence of networks with power-law degree distributions. It is then quite important to determine if this mechanism is the consequence of a…
We analyze growing networks that are built by enhanced redirection. Nodes are sequentially added and each incoming node attaches to a randomly chosen 'target' node with probability 1-r, or to the parent of the target node with probability…
The Watts-Strogatz algorithm transferring a regular lattice to the small world network is modified by introducing preferential rewiring constrained by connectivity demand. The probability to link to/ unlink form a node is dependent on a…
We propose a simple preferential attachment model of growing network using the complementary probability of Barab\'asi-Albert (BA) model, i.e., $\Pi(k_i) \propto 1-\frac{k_i}{\sum_j k_j}$. In this network, new nodes are preferentially…
We introduce a broad class of multi-hooking networks, wherein multiple copies of a seed are hooked at each step at random locations, and the number of copies follows a predetermined building sequence of numbers. We analyze the degree…
We introduce a new model of competition on growing networks. This extends the preferential attachment model, with the key property that node choices evolve simultaneously with the network. When a new node joins the network, it chooses…
Complex networks have abundant and extensive applications in real life. Recently, researchers have proposed a number of complex networks, in which some are deterministic and others are random. Compared with deterministic networks, random…
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 study an asymptotical behavior of the maximal degree in the degree distribution in an evolving tree model combining the local choice and the Mori's preferential attachment. In the considered model, the random graph is constructed in the…