Related papers: Raising Graphs From Randomness to Reveal Informati…
In this note we make some specific observations on the distribution of the degree of a given vertex in certain model of randomly growing networks. The rule for network growth is the following. Starting with an initial graph of minimum…
The multiplex network growth literature has been confined to homogeneous growth hitherto, where the number of links that each new incoming node establishes is the same across layers. This paper focuses on heterogeneous growth. We first…
The probability distribution of number of ties of an individual in a social network follows a scale-free power-law. However, how this distribution arises has not been conclusively demonstrated in direct analyses of people's actions in…
The community structure and motif-modular-network hierarchy are of great importance for understanding the relationship between structures and functions. In this paper, we investigate the distribution of clique-degree, which is an extension…
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…
Network growth is currently explained through mechanisms that rely on node prestige measures, such as degree or fitness. In many real networks those who create and connect nodes do not know the prestige values of existing nodes, but only…
Ever since the Barab\'{a}si-Albert (BA) scale-free network has been proposed, network modeling has been studied intensively in light of the network growth and the preferential attachment (PA). However, numerous real systems are featured…
Recently several authors have proposed stochastic evolutionary models for the growth of the web graph and other networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to…
This study examines degree distributions in two large collaboration networks: the Microsoft Academic Graph (1800-2020) and Internet Movie Database (1900-2020), comprising $2.72 \times 10^8$ and $1.88 \times 10^6$ nodes respectively.…
We introduce a network evolution process motivated by the network of citations in the scientific literature. In each iteration of the process a node is born and directed links are created from the new node to a set of target nodes already…
We generalize an algorithm used widely in the configuration model such that power-law degree sequences with the degree exponent $\lambda$ and the number of links per node $K$ controllable independently may be generated. It yields the degree…
In a recent paper, Krapivsky and Redner (Phys. Rev. E, 71 (2005) 036118) proposed a new growing network model with new nodes being attached to a randomly selected node, as well to all ancestors of the target node. The model leads to a…
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,…
We model the evolution of the Internet at the Autonomous System level as a process of competition for users and adaptation of bandwidth capability. We find the exponent of the degree distribution as a simple function of the growth rates of…
Degree distributions of many real networks are known to follow the Mandelbrot law, which can be considered as an extension of the power law and is determined by not only the power-law exponent, but also the shifting coefficient. Although…
Various important and useful quantities or measures that characterize the topological network structure are usually investigated for a network, then they are averaged over the samples. In this paper, we propose an explicit representation by…
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…
The degree distribution of many biological and technological networks has been described as a power-law distribution. While the degree distribution does not capture all aspects of a network, it has often been suggested that its functional…
We include complex connectivity structures and heterogeneity in models of multilayer networks or multilayer hypergraphs growing by preferential attachment. We consider the most generic connectivity structure, where the probability of…
The degree distribution is a key statistical indicator in network theory, often used to understand how information spreads across connected nodes. In this paper, we focus on non-growing networks formed through a rewiring algorithm and…