Signal propagation in complex networks drives epidemics, is responsible for information
going viral, promotes trust and facilitates moral behavior in social groups, enables the …

In the last two decades, network science has blossomed and influenced various fields, such
as statistical physics, computer science, biology and sociology, from the perspective of the …

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 …

Over the past two decades percolation theory has been used to explain and model a wide
variety of phenomena that are of industrial and scientific importance. Examples include …

We derive rigorous asymptotic results for the magnitude of contagion in a large counterparty
network and give an analytical expression for the asymptotic fraction of defaults, in terms of …

In $ r $-neighbour bootstrap percolation on a graph $ G $, a (typically random) set $ A $ of
initially 'infected'vertices spreads by infecting (at each time step) vertices with at least $ r …

Bootstrap percolation on the random graph G_n,p is a process of spread of “activation” on a
given realization of the graph with a given number of initially active nodes. At each step …

This slim volume logs the development of a cascade of contagious ideas that has occupied
my space, time and mind in recent years. There was a clear triggering event that occurred in …

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 …

Given a family of (hyper) graphs $\mathcal {F} $ a (hyper) graph $ G $ is said to be $\mathcal
{F} $-saturated if $ G $ is $ F $-free for any $ F\in\mathcal {F} $ but for any edge e in the …