Related papers: Percolation transition in networks with degree-deg…
Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here,…
Real-world networks often exhibit strong transitivity with nontrivial local clustering spectra and degree correlations. Such features are not easily modeled in tractable network models, creating an obstacle to the theoretical understanding…
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…
We study the effect of assortative and disassortative mixing on the robustness of networks under random node failures. For ordinary (dyadic) networks, by using the generating function technique and stochastic simulations, we show that the…
We present a generator of random networks where both the degree-dependent clustering coefficient and the degree distribution are tunable. Following the same philosophy as in the configuration model, the degree distribution and the…
We present exact analysis of the physical properties of bimodal networks specified by the two peak degree distribution fully incorporating the degree-degree correlation between node connection. The structure of the correlated bimodal…
Biased (degree-dependent) percolation was recently shown to provide new strategies for turning robust networks fragile and vice versa. Here we present more detailed results for biased edge percolation on scale-free networks. We assume a…
In a recent Letter, Friedman and Landsberg discussed the underlying mechanism of explosive phase transitions on complex networks [Phys. Rev. Lett. 103, 255701 (2009)]. This Brief Report presents a modest, though more insightful extension of…
We discuss three related models of scale-free networks with the same degree distribution but different correlation properties. Starting from the Barabasi-Albert construction based on growth and preferential attachment we discuss two other…
Exponential random graphs are important to model the structure of real-world complex networks. Here we solve the two-star model with degree-degree correlations in the sparse regime. The model constraints the average correlation between the…
Yang, Wang, and Motter [Phys. Rev. Lett. 109, 258701 (2012)] analyzed a model for network observability transitions in which a sensor placed on a node makes the node and the adjacent nodes observable. The size of the connected components…
We consider robustness and percolation properties of the networks of networks, in which random nodes in different individual networks (layers) can be interdependent. We explore the emergence of the giant mutually connected component,…
Complex networks have been mostly characterized from the point of view of the degree distribution of their nodes and a few other motifs (or modules), with a special attention to triangles and cliques. The most exotic phenomena have been…
Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…
Transition points mark qualitative changes in the macroscopic properties of large complex systems. Explosive transitions, exhibiting properties of both continuous and discontinuous phase transitions, have recently been uncovered in network…
We present analytical results for the structural evolution of random networks undergoing contraction processes via generic node deletion scenarios, namely, random deletion, preferential deletion and propagating deletion. Focusing on…
Percolation is perhaps the simplest example of a process exhibiting a phase transition and one of the most studied phenomena in statistical physics. The percolation transition is continuous if sites/bonds are occupied independently with the…
Recently, new results on percolation of interdependent networks have shown that the percolation transition can be first order. In this paper we show that, when considering antagonistic interactions between interacting networks, the…
While degree correlations are known to play a crucial role for spreading phenomena in networks, their impact on the propagation speed has hardly been understood. Here we investigate a tunable spreading model on scale-free networks and show…
We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks…