A Central Limit Theorem for Diffusion in Sparse Random Graphs

by   Hamed Amini, et al.

We consider bootstrap percolation and diffusion in sparse random graphs with fixed degrees, constructed by configuration model. Every node has two states: it is either active or inactive. We assume that to each node is assigned a nonnegative (integer) threshold. The diffusion process is initiated by a subset of nodes with threshold zero which consists of initially activated nodes, whereas every other node is inactive. Subsequently, in each round, if an inactive node with threshold θ has at least θ of its neighbours activated, then it also becomes active and remains so forever. This is repeated until no more nodes become activated. The main result of this paper provides a central limit theorem for the final size of activated nodes. Namely, under suitable assumptions on the degree and threshold distributions, we show that the final size of activated nodes has asymptotically Gaussian fluctuations.



There are no comments yet.


page 1

page 2

page 3

page 4


Parameterized Complexity of Immunization in the Threshold Model

We consider the problem of controlling the spread of harmful items in ne...

Target Set in Threshold Models

Consider a graph G and an initial coloring, where each node is blue or r...

Spread of Influence in Graphs

Consider a graph G and an initial configuration where each node is black...

Time-Bounded Influence Diffusion with Incentives

A widely studied model of influence diffusion in social networks represe...

Asymptotic degree distributions in random threshold graphs

We discuss several limiting degree distributions for a class of random t...

Locality of Random Digraphs on Expanders

We study random digraphs on sequences of expanders with bounded average ...

Heat diffusion distance processes: a statistically founded method to analyze graph data sets

We propose two multiscale comparisons of graphs using heat diffusion, al...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.