Related papers: Explosive percolation in scale-free networks
A Barab\'asi-Albert scale-free network is constructed whose nodes are the Poisson distributed random points within a unit square and links are the straight line connections among the nodes. The cost function, which is the total wiring…
Uncorrelated random scale-free networks are useful null models to check the accuracy an the analytical solutions of dynamical processes defined on complex networks. We propose and analyze a model capable to generate random uncorrelated…
We study the percolation in coupled networks with both inner-dependency and inter-dependency links, where the inner- and inter-dependency links represent the dependencies between nodes in the same or different networks, respectively. We…
Many real systems exhibit the processes of growth and shrink. In this paper, we propose a network evolution model based on the simultaneous application of both node addition and deletion rules. To obtain a higher clustering that is present…
We discuss how various models of scale-free complex networks approach their limiting properties when the size N of the network grows. We focus mainly on equilibrated networks and their finite-size degree distributions. Our results show that…
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…
Explosive percolation in the Achlioptas process has recently attracted much research attention. From extensive simulations in an event-based ensemble, we find that, in dimensions from $2$ to $6$ and on random graphs, the Achlioptas…
We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…
Several studies on real complex networks from different fields as biology, economy, or sociology have shown that the degree of nodes (number of edges connected to each node) follows a scale-free power-law distribution like $P(k)\approx…
Assign to each vertex of the one-dimensional torus i.i.d. weights with a heavy-tail of index $\tau-1>0$. Connect then each couple of vertices with probability roughly proportional to the product of their weights and that decays polynomially…
Clusters generated by the product-rule growth model of Achlioptas, D'Souza, and Spencer on a two-dimensional square lattice are shown to obey qualitatively different scaling behavior than standard (random growth) percolation. The threshold…
A majority of studied models for scale-free networks have degree distributions with exponents greater than $2$. Real networks, however, can demonstrate essentially more heavy-tailed degree distributions. We explore two models of scale-free…
In this work we investigate the spectra of Laplacian matrices that determine many dynamic properties of scale-free networks below and at the percolation threshold. We use a replica formalism to develop analytically, based on an integral…
Synchronization problems in complex networks are very often studied by researchers due to its many applications to various fields such as neurobiology, e-commerce and completion of tasks. In particular, Scale Free networks with degree…
We study scale free simple graphs with an exponent of the degree distribution $\gamma$ less than two. Generically one expects such extremely skewed networks -- which occur very frequently in systems of virtually or logically connected units…
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…
It is a mainstream idea that scale-free network would be fragile under the selective attacks. Internet is a typical scale-free network in the real world, but it never collapses under the selective attacks of computer viruses and hackers.…
We apply a variant of the explosive percolation procedure to large real-world networks, and show with finite-size scaling that the university class, ordinary or explosive, of the resulting percolation transition depends on the structural…
Random scale-free networks have the peculiar property of being prone to the spreading of infections. Here we provide an exact result showing that a scale-free connectivity distribution with diverging second moment is a sufficient condition…
The parallel computational complexity or depth of growing network models is investigated. The networks considered are generated by preferential attachment rules where the probability of attaching a new node to an existing node is given by a…