The emergence of large-scale connectivity and synchronization are crucial to the structure,
function and failure of many complex socio-technical networks. Thus, there is great interest …

Percolation and synchronization are two phase transitions that have been extensively
studied since already long ago. A classic result is that, in the vast majority of cases, these …

The emergence of large-scale connectivity on an underlying network or lattice, the so-called
percolation transition, has a profound impact on the system's macroscopic behaviours …

Explosive collective phenomena have attracted much attention since the discovery of an
explosive percolation transition. In this Letter, we demonstrate how an explosive transition …

Networks in which the formation of connections is governed by a random process often
undergo a percolation transition, wherein around a critical point, the addition of a small …

Percolation is the simplest fundamental model in statistical mechanics that exhibits phase
transitions signaled by the emergence of a giant connected component. Despite its very …

Critical transitions are observed in many complex systems. This includes the onset of
synchronization in a network of coupled oscillators or the emergence of an epidemic state …

How a complex network is connected crucially impacts its dynamics and function.
Percolation, the transition to extensive connectedness on gradual addition of links, was long …

The internal organization of complex networks often has striking consequences on either
their response to external perturbations or on their dynamical properties. In addition to small …

Percolation is one of the most studied processes in statistical physics. A recent paper by
Achlioptas et al.[Science 323, 1453 (2009)] showed that the percolation transition, which is …