Related papers: A Generalized Preferential Attachment Model for Co…
Preferential attachment models have been widely studied in complex networks, because they can explain the formation of many networks like social networks, citation networks, power grids, and biological networks, to name a few. Motivated by…
In this paper, we propose a growing random complex network model, which we call context dependent preferential attachment model (CDPAM), when the preference of a new node to get attached to old nodes is determined by the local and global…
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,…
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…
The mechanism of preferential attachment underpins most recent social network formation models. Yet few authors attempt to check or quantify assumptions on this mechanism. We call generalized preferential attachment any kind of preference…
Identifying the generating mechanism of a network is challenging as, more often than not, only snapshots are available, but not the full evolution. One candidate for the generating mechanism is preferential attachment which, in its simplest…
We consider a general preferential attachment model, where the probability that a newly arriving vertex connects to an older vertex is proportional to a sublinear function of the indegree of the older vertex at that time. It is well known…
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 consider a preferential growth model where particles are added one by one to the system consisting of clusters of particles. A new particle can either form a new cluster (with probability q) or join an already existing cluster with a…
Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get…
Many important real-world networks manifest "small-world" properties such as scale-free degree distributions, small diameters, and clustering. The most common model of growth for these networks is "preferential attachment", where nodes…
Critical, or scale independent, systems are so ubiquitous, that gaining theoretical insights on their nature and properties has many direct repercussions in social and natural sciences. In this report, we start from the simplest possible…
In spite of its relevance to the origin of complex networks, the interplay between form and function and its role during network formation remains largely unexplored. While recent studies introduce dynamics by considering rewiring processes…
We study a model for the evolution of chemical species under a combination of population dynamics on a short time scale and a selection mechanism on a longer time scale. Least fit nodes are replaced by new nodes whose links are attached to…
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…
The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
We obtain closed form expressions for the expected conditional degree distribution and the joint degree distribution of the linear preferential attachment model for network growth in the steady state. We consider the multiple-destination…
Many networks exhibit scale free behavior where their degree distribution obeys a power law for large vertex degrees. Models constructed to explain this phenomena have relied on preferential attachment where the networks grow by the…
Many complex systems have been shown to share universal properties of organization, such as scale independence, modularity and self-similarity. We borrow tools from statistical physics in order to study structural preferential attachment…
We introduce a network growth model in which the preferential attachment probability includes the fitness vertex and the Euclidean distance between nodes. We grow a planar network around its barycenter. Each new site is fixed in space by…