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Burning a Graph as a Model of Social Contagion
[chapter]

2014
*
Lecture Notes in Computer Science
*

The

doi:10.1007/978-3-319-13123-8_2
fatcat:446smow3i5bjbcz7gehf2a34na
*burning*number measures the speed*of*the spread*of**contagion*in*a**graph*; the lower the*burning*number, the faster the*contagion*spreads. ... The*burning*number is computed for several*graph*classes, and is derived for the*graphs*generated by the Iterated Local Transitivity*model*for*social*networks. ... Conclusions and future work We introduced*a*new*graph*parameter, the*burning*number*of**a**graph*, written b(G). The*burning*number measures how rapidly*social**contagion*spreads in*a*given*graph*. ...##
###
How to Burn a Graph

2015
*
Internet Mathematics
*

The

doi:10.1080/15427951.2015.1103339
fatcat:qmoqyjz2pvgrbmbpqkhszefn2y
*burning*number measures the speed*of*the spread*of**contagion*in*a**graph*; the lower the*burning*number, the faster the*contagion*spreads. ... The*burning*number is computed for several*graph*classes, and is derived for the*graphs*generated by the Iterated Local Transitivity*model*for*social*networks. ...*Burning*may be viewed*as**a*simplified*model*for the spread*of**social**contagion*in*a**social*network such*as*Facebook or Twitter. ...##
###
How to burn a graph
[article]

2015
*
arXiv
*
pre-print

The

arXiv:1507.06524v1
fatcat:uqfcs3cmd5dz7imqqctvyiqry4
*burning*number measures the speed*of*the spread*of**contagion*in*a**graph*; the lower the*burning*number, the faster the*contagion*spreads. ... The*burning*number is computed for several*graph*classes, and is derived for the*graphs*generated by the Iterated Local Transitivity*model*for*social*networks. ...*Burning*may be viewed*as**a*simplified*model*for the spread*of**social**contagion*in*a**social*network such*as*Facebook or Twitter. ...##
###
Burning a graph is hard

2017
*
Discrete Applied Mathematics
*

The

doi:10.1016/j.dam.2017.07.016
fatcat:n5hpmiwmd5dxlhcqozii2gmo4m
*burning*number measures the speed*of*the spread*of**contagion*in*a**graph*; the lower the*burning*number, the faster the*contagion*spreads. ... We introduce*a*new*graph*parameter called the*burning*number, inspired by contact processes on*graphs*such*as**graph*bootstrap percolation, and*graph*searching paradigms such*as*Firefighter. ...*Burning*may be viewed*as**a*simplified*model*for the spread*of**social**contagion*in*a**social*network such*as*Facebook or Twitter. ...##
###
Burning graphs through farthest-first traversal
[article]

2021
*
arXiv
*
pre-print

The

arXiv:2011.15019v4
fatcat:6ntrjvx6unhmfpdvlhbsuxpcoy
*graph**burning*problem is an NP-hard combinatorial optimization problem that helps quantify the vulnerability*of**a**graph*to*contagion*. ... This paper introduces*a*simple farthest-first traversal-based approximation algorithm for this problem over general*graphs*. We refer to this proposal*as*the*Burning*Farthest-First (BFF) algorithm. ... Roshanbin,*Burning**a**graph**as**a**model**of**social**contagion*, in: International Workshop on Algorithms and*Models*for the Web-*Graph*, Springer, 2014, pp. 13-22 [2] M. Šimon, L. Huraj, I. ...##
###
Approximation Algorithms for Graph Burning
[article]

2019
*
arXiv
*
pre-print

Numerous approaches study the vulnerability

arXiv:1811.04449v2
fatcat:jcqhaua2rjdmplmjs67mywtfjy
*of*networks against*social**contagion*.*Graph**burning*studies how fast*a**contagion*,*modeled**as**a*set*of*fires, spreads in*a**graph*. ... Given*a**graph*, the objective*of*an algorithm is to find*a*schedule that minimizes the number*of*rounds to*burn**graph*. ... [5, 6] first introduced the*burning*process*as**a*way to*model*spread*of**contagion*in*a**social*network; they characterized the*burning*number for some*graph*classes and proved some properties for the ...##
###
APX-Hardness and Approximation for the k-Burning Number Problem
[article]

2021
*
arXiv
*
pre-print

The 1-

arXiv:2006.14733v2
fatcat:fiuxovnyzjh7dmvgyxbesxk3wm
*burning*number coincides with the well-known*burning*number problem, which was proposed to*model*the spread*of**social**contagion*. ... Consider an information diffusion process on*a**graph*G that starts with k>0 burnt vertices, and at each subsequent step,*burns*the neighbors*of*the currently burnt vertices,*as*well*as*k other unburnt ... [6, 7] , provides*a*simple*model*for such*a**social**contagion*process. ...##
###
The Burning Number of Directed Graphs: Bounds and Computational Complexity
[article]

2020
*
arXiv
*
pre-print

The

arXiv:2001.03381v1
fatcat:d7jq2mojcjcatdbwd6ypmmafzq
*burning*number*of**a**graph*was recently introduced by Bonato et al. ... Here, we introduce*graph**burning*for directed*graphs*, and we study bounds for the corresponding*burning*number and the hardness*of*finding this number. ... The author would like to thank Josse van Dobben de Bruyn for bringing*graph**burning*to his attention, and Mark Jones for lending his expertise in parametrized complexity. ...##
###
Bayesian Analysis of Social Influence
[article]

2022
*
arXiv
*
pre-print

The basic influence

arXiv:2006.16464v3
fatcat:u6rgceft2rbajdx6bmzpejljzy
*model*was previously extended to afford*a*suite*of*new dependence assumptions and because*of*its relation to traditional Markov random field*models*it is often referred to*as*the auto ... The network influence*model*is*a**model*for binary outcome variables that accounts for dependencies between outcomes for units that are relationally tied. ... We are grateful for comments on early drafts by*a*number*of*people at IC 2 S 2 and ARS'19,*as*well*as*researchers that have patiently tested the inference procedure: Bella Vartanyan, the Science*of*Networks ...##
###
Spread and defend infection in graphs
[article]

2021
*
arXiv
*
pre-print

*Graph*

*burning*simulates the notion

*of*the spread

*of*"fire" throughout

*a*

*graph*(plus, one unburned node

*burned*at each time-step);

*graph*firefighting simulates the defending

*of*nodes by placing firefighters ... This article studies

*a*combination

*of*firefighting and

*burning*on

*a*

*graph*class which is

*a*variation (generalization)

*of*temporal

*graphs*. Nodes can be infected from "outside"

*a*network. ... This makes

*graph*

*burning*[6] and wburning [33] special cases

*of*this

*model*where

*a*constant number

*of*nodes are

*burned*from outside. ...

##
###
Bounds on the burning numbers of spiders and path-forests
[article]

2017
*
arXiv
*
pre-print

*Graph*

*burning*is one

*model*for the spread

*of*memes and

*contagion*in

*social*networks. ... The corresponding

*graph*parameter is the

*burning*number

*of*

*a*

*graph*$G$, written $b(G)$, which measures the speed

*of*the

*social*

*contagion*. ... The

*burning*number

*of*

*a*

*graph*was introduced

*as*

*a*simple

*model*

*of*spreading memes or other kinds

*of*

*social*

*contagion*in [3, 7] . ...

##
###
New heuristics for burning graphs
[article]

2020
*
arXiv
*
pre-print

*Graph*

*burning*

*models*the spread

*of*

*contagion*(fire) in

*a*

*graph*in discrete time steps. bn(G) is the minimum time needed to

*burn*

*a*

*graph*G.The problem is NP-complete. ... The concept

*of*

*graph*

*burning*and

*burning*number (bn(G))

*of*

*a*

*graph*G was introduced recently [1]. ... Since the problem is

*modeling*the spread

*of*

*contagion*in

*a*network, it is essential to develop algorithms for solving the problem. We developed 6 heuristics for

*burning*

*a*

*graph*. ...

##
###
Burning Two Worlds: Algorithms for Burning Dense and Tree-like Graphs
[article]

2019
*
arXiv
*
pre-print

*Graph*

*burning*is

*a*simple

*model*for the spread

*of*

*social*influence in networks. The objective is to measure how quickly

*a*fire (e.g.,

*a*piece

*of*fake news) can be spread in

*a*network. ... The

*burning*problem is known to be NP-hard even when the

*graph*is

*a*tree or

*a*disjoint set

*of*paths. For connected

*graphs*, it has been conjectured that

*burning*takes at most √(n) rounds. ... Previous work The

*graph*

*burning*problem was introduced by Bonato et al. [3, 4]

*as*

*a*way to

*model*the spread

*of*

*a*

*contagion*in

*social*networks. Bonato et al. ...

##
###
Improved Bounds for Burning Fence Graphs
[article]

2019
*
arXiv
*
pre-print

*Graph*

*burning*studies how fast

*a*

*contagion*,

*modeled*

*as*

*a*set

*of*fires, spreads in

*a*

*graph*. The

*burning*process takes place in synchronous, discrete rounds. ... The

*burning*number

*of*

*a*

*graph*G is the minimum number

*of*rounds necessary for each vertex

*of*G to

*burn*. We consider the

*burning*number

*of*the m × n Cartesian grid

*graphs*, written G_m,n. ... Introduction

*Graph*

*burning*was introduced in [4, 5] to

*model*the spread

*of*

*social*

*contagion*, such

*as*rumors, gossip, or memes in

*a*network. ...

##
###
Burning a Graph is Hard
[article]

2015
*
arXiv
*
pre-print

*Graph*

*burning*is

*a*

*model*for the spread

*of*

*social*

*contagion*. ... The

*burning*number is

*a*

*graph*parameter associated with

*graph*

*burning*that measures the speed

*of*the spread

*of*

*contagion*in

*a*

*graph*; the lower the

*burning*number, the faster the

*contagion*spreads. ...

*Graph*

*burning*is

*a*simplified deterministic

*model*for the spread

*of*

*social*

*contagion*in

*a*

*social*network that considers an answer to these questions, and was introduced in [2] . ...

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