We consider the following activation process in undirected graphs: a vertex is active either if
it belongs to a set of initially activated vertices or if at some point it has at least r active …

Consider a graph G and an initial configuration, where each node is black or white. Assume
that in discrete-time rounds, all nodes simultaneously update their color based on a …

We study the activation process in undirected graphs known as bootstrap percolation: a
vertex is active either if it belongs to a set of initially activated vertices or if at some point it …

For fixed r≥ 2, we consider bootstrap percolation with threshold r on the Erdős–Rényi graph
𝓖 n, p. We identify a threshold for p above which there is with high probability a set of size r …

The-complex contagion model is a social contagion model which describes the diffusion of
behaviors in networks where the successful adoption of a behavior requires influence from …

Complex contagions describe diffusion of behaviors in a social network in settings where
spreading requires influence by two or more neighbors. In ak-complex contagion, a cluster …

There are hundreds of online social networks with billions of users in total. Many such
networks publicly release structural information, with all personal information removed …

We study the following bootstrap percolation process: given a connected graph G, a
constant ρ∈[0, 1] and an initial set A⊆ V (G) of infected vertices, at each step a vertex v …

In this paper we analyze k-complex contagions (sometimes called bootstrap percolation) on
configuration model graphs with a power-law distribution. Our main result is that if the power …

Kleinberg's small world model 20 simulates social networks with both strong and weak ties.
In his original paper, Kleinberg showed how the distribution of weak-ties, parameterized by γ …