Related papers: Early warning signals for phase transitions in net…
A tipping point can be defined as an abrupt shift in the properties or behaviour of a system. Tipping points in complex systems from a wide variety of scientific disciplines have been compared to phase transitions in physics, but consistent…
Bond percolation on infinite heavy-tailed power-law random networks lacks a proper phase transition; or one may say, there is a phase transition at {\em zero percolation probability}. Nevertheless, a finite size percolation threshold…
We study the problem of identifying macroscopic structures in networks, characterizing the impact of introducing link directions on the detectability phase transition. To this end, building on the stochastic block model, we construct a…
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…
The critical boundaries separating ordered from chaotic behavior in randomly wired S-state networks are calculated. These networks are a natural generalization of random Boolean nets and are proposed as on extended approach to genetic…
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…
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…
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…
The connectivity of individual neurons of large neural networks determine both the steady state activity of the network and its answer to external stimulus. Highly diluted random networks have zero activity. We show that increasing the…
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 consider bootstrap percolation on uncorrelated complex networks. We obtain the phase diagram for this process with respect to two parameters: $f$, the fraction of vertices initially activated, and $p$, the fraction of undamaged vertices…
Interactions among people or objects are often dynamic in nature and can be represented as a sequence of networks, each providing a snapshot of the interactions over a brief period of time. An important task in analyzing such evolving…
Change-point detection methods are proposed for the case of temporary failures, or transient changes, when an unexpected disorder is ultimately followed by a readjustment and return to the initial state. A base distribution of the…
Many social, biological, and economic systems can be approached by complex networks of interacting units. The behaviour of several models on small-world networks has recently been studied. These models are expected to capture the essential…
Recent advances have shown that introducing dependency interactions between two superconducting networks can trigger abrupt, hysteretic normal-superconductor phase transitions. In this study, we demonstrate that such behavior can also arise…
We present an exact solution of percolation in a generalized class of Watts-Strogatz graphs defined on a 1-dimensional underlying lattice. We find a non-classical critical point in the limit of the number of long-range bonds in the system…
We introduce the concept of network susceptibilities quantifying the response of the collective dy- namics of a network to small parameter changes. We distinguish two types of susceptibilities: vertex susceptibilities and edge…
The study of interdependent networks, and in particular the robustness on networks, has attracted considerable attention. Recent studies mainly assume that the dependence is fully interdependent. However, targeted attack for partially…
Generative, temporal network models play an important role in analyzing the dependence structure and evolution patterns of complex networks. Due to the complicated nature of real network data, it is often naive to assume that the underlying…
Recently, the percolation transition has been characterized on interacting networks both in presence of interdependent and antagonistic interactions. Here we characterize the phase diagram of the percolation transition in two Poisson…