Related papers: Degree distributions under general node removal: P…
The "power of choice" has been shown to radically alter the behavior of a number of randomized algorithms. Here we explore the effects of choice on models of tree and network growth. In our models each new node has k randomly chosen…
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 introduce a growing network model---the copying model---in which a new node attaches to a randomly selected target node and, in addition, independently to each of the neighbors of the target with copying probability $p$. When…
After a failure or attack the structure of a complex network changes due to node removal. Here, we show that the degree distribution of the distorted network, under any node disturbances, can be easily computed through a simple formula.…
In this paper, we provide a general method to obtain the exact solutions of the degree distributions for RBDN with network size decline. First by stochastic process rules, the steady state transformation equations and steady state degree…
We analyze the properties of Degree-Ordered Percolation (DOP), a model in which the nodes of a network are occupied in degree-descending order. This rule is the opposite of the much studied degree-ascending protocol, used to investigate…
Correlations may affect propagation processes on complex networks. To analyze their effect, it is useful to build ensembles of networks constrained to have a given value of a structural measure, such as the degree-degree correlation $r$,…
In this paper, we study a class of stochastic processes, called evolving network Markov chains, in evolving networks. Our approach is to transform the degree distribution problem of an evolving network to a corresponding problem of evolving…
Delaunay triangulation can be considered as a type of complex networks. For complex networks, the degree distribution is one of the most important inherent characteristics. In this paper, we first consider the two- and three-dimensional…
The power law is useful in describing count phenomena such as network degrees and word frequencies. With a single parameter, it captures the main feature that the frequencies are linear on the log-log scale. Nevertheless, there have been…
Scale-free networks with small power law exponent are known to be robust, meaning that their qualitative topological structure cannot be altered by random removal of even a large proportion of nodes. By contrast, it has been argued in the…
Understanding the structure of the Internet graph is a crucial step for building accurate network models and designing efficient algorithms for Internet applications. Yet, obtaining its graph structure is a surprisingly difficult task, as…
Evolving network models under a dynamic growth rule which comprises the addition and deletion of nodes are investigated. By adding a node with a probability $P_a$ or deleting a node with the probability $P_d=1-P_a$ at each time step, where…
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…
We focus on the role played by the node degree distribution on the way collective phenomena emerge on complex networks. To address this question, we focus analytically on a typical model for cooperative behaviour, the Majority Rule, applied…
We consider large networks of theta neurons and use the Ott/Antonsen ansatz to derive degree-based mean field equations governing the expected dynamics of the networks. Assuming random connectivity we investigate the effects of varying the…
We present a general holistic theory for the organization of complex networks, both human-engineered and naturally-evolved. Introducing concepts of value of interactions and satisfaction as generic network performance measures, we show that…
It is commonly believed that scale-free networks are robust to massive numbers of random node deletions. For example, Cohen et al. study scale-free networks including some which approximate the measured degree distribution of the Internet.…
We present analytical results for the emerging structure of networks that evolve via a combination of growth (by node addition and random attachment) and contraction (by random node deletion). To this end we consider a network model in…
There is great interest in predicting rare and extreme events in complex systems, and in particular, understanding the role of network topology in facilitating such events. In this work, we show that degree dispersion -- the fact that the…