Related papers: Degree Correlation in Scale-Free Graphs
The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree…
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…
Barab\'asi-Albert's `Scale Free' model is the starting point for much of the accepted theory of the evolution of real world communication networks. Careful comparison of the theory with a wide range of real world networks, however,…
The network properties of a graph ensemble subject to the constraints imposed by the expected degree sequence are studied. It is found that the linear preferential attachment is a fundamental rule, as it keeps the maximal entropy in sparse…
Preferential attachment is a popular model of growing networks. We consider a generalized model with random node removal, and a combination of preferential and random attachment. Using a high-degree expansion of the master equation, we…
Complex systems can be characterized by classes of equivalency of their elements defined according to system specific rules. We propose a generalized preferential attachment model to describe the class size distribution. The model…
Based on the empirical analysis of the dependency network in 18 Java projects, we develop a novel model of network growth which considers both: an attachment mechanism and the addition of new nodes with a heterogeneous distribution of their…
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…
The random graph model has recently been extended to a random preferential attachment graph model, in order to enable the study of general asymptotic properties in network types that are better represented by the preferential attachment…
We propose a rate equation approach to compute two vertex correlations in scale-free growing network models based in the preferential attachment mechanism. The formalism, based on previous work of Szab\'o \textit{et al.} [Phys. Rev. E…
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…
Different types of interactions coexist and coevolve to shape the structure and function of a multiplex network. We propose here a general class of growth models in which the various layers of a multiplex network coevolve through a set of…
The article deals with two classes of growing random graphs following the preferential attachment rule with a linear weight function, L-graphs, and hybrid Pennock graphs. We determine the exact final vertex degree distribution and the exact…
Models based on preferential attachment have had much success in reproducing the power law degree distributions which seem ubiquitous in both natural and engineered systems. Here, rather than assuming preferential attachment, we give an…
The in-degree and out-degree distributions of a growing network model are determined. The in-degree is the number of incoming links to a given node (and vice versa for out-degree. The network is built by (i) creation of new nodes which each…
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…
A key ingredient of current models proposed to capture the topological evolution of complex networks is the hypothesis that highly connected nodes increase their connectivity faster than their less connected peers, a phenomenon called…
Preferential attachment is one possible way to obtain a scale-free network. We develop a self-consistent method to determine whether preferential attachment occurs during the growth of a network, and to extract the preferential attachment…
We introduce a collection of complex networks generated by a combination of preferential attachment and a previously unexamined process of "splitting" nodes of degree $k$ into $k$ nodes of degree 1. Four networks are considered, each…
We extend the classical preferential attachment random graph model to random simplicial complexes. At each stage of the model, we choose one of the existing $k$-simplices with probability proportional to its $k$-degree. The chosen…