Related papers: Critical phenomena in networks
We report numerical evidence that an epidemic-like model, which can be interpreted as the propagation of a rumor, exhibits critical behavior at a finite randomness of the underlying small-world network. The transition occurs between a…
The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects dramatically different from those in cooperative systems on lattices. In the last few years,…
We consider critical phenomena on heterogeneous small-world networks having a scale-free character but also arbitrary short-loops. After deriving the self-consistent equation for the order parameter and the critical surface, we prove that…
A classification of critical behavior is provided in systems for which the renormalization group equations are control-parameter dependent. It describes phase transitions in networks with a recursive, hierarchical structure but appears to…
We show that a simple model for the propagation of a rumor on a small-world network exhibits critical behavior at a finite randomness of the underlying graph. The transition occurs between a regime where the rumor "dies" in a small…
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…
We analyze critical phenomena on networks generated as the union of hidden variables models (networks with any desired degree sequence) with arbitrary graphs. The resulting networks are general small-worlds similar to those a` la Watts and…
Motivated by the idea that criticality and universality of phase transitions might play a crucial role in achieving and sustaining learning and intelligent behaviour in biological and artificial networks, we analyse a theoretical and a…
Within the conventional statistical physics framework, we study critical phenomena in a class of configuration network models with hidden variables controlling links between pairs of nodes. We find analytical expressions for the average…
Critical behavior of the contact process is studied in annealed scale-free networks by mapping it on the random walk problem. We obtain the analytic results for the critical scaling, using the event-driven dynamics approach. These results…
We provide a framework for determining the centralities of agents in a broad family of random networks. Current understanding of network centrality is largely restricted to deterministic settings, but practitioners frequently use random…
Weighted scale-free networks with topology-dependent interactions are studied. It is shown that the possible universality classes of critical behaviour, which are known to depend on topology, can also be explored by tuning the form of the…
Standard Random Boolean Networks display an order-disorder phase transition. We add to the standard Random Boolean Networks a disconnection rule which couples the control and order parameters. By this way, the system is driven to the…
We evolve network topology of an asymmetrically connected threshold network by a simple local rewiring rule: quiet nodes grow links, active nodes lose links. This leads to convergence of the average connectivity of the network towards the…
We discuss the complex dynamics of a non-linear random networks model, as a function of the connectivity k between the elements of the network. We show that this class of networks exhibit an order-chaos phase transition for a critical…
Network structure strongly constrains the range of dynamic behaviors available to a complex system. These system dynamics can be classified based on their response to perturbations over time into two distinct regimes, ordered or chaotic,…
Spreading phenomena on networks are essential for the collective dynamics of various natural and technological systems, from information spreading in gene regulatory networks to neural circuits or from epidemics to supply networks…
Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical…
An anomalous mean-field solution is known to capture the non trivial phase diagram of the Ising model in annealed complex networks. Nevertheless the critical fluctuations in random complex networks remain mean-field. Here we show that a…
Many real-world systems can be expressed in temporal networks with nodes playing far different roles in structure and function and edges representing the relationships between nodes. Identifying critical nodes can help us control the spread…