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

Anthony Bonato, Jeannette Janssen, Elham Roshanbin
2014 Lecture Notes in Computer Science  
The 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.  ... 
doi:10.1007/978-3-319-13123-8_2 fatcat:446smow3i5bjbcz7gehf2a34na

How to Burn a Graph

Anthony Bonato, Jeannette Janssen, Elham Roshanbin
2015 Internet Mathematics  
The 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.  ... 
doi:10.1080/15427951.2015.1103339 fatcat:qmoqyjz2pvgrbmbpqkhszefn2y

How to burn a graph [article]

Anthony Bonato, Jeannette Janssen, Elham Roshanbin
2015 arXiv   pre-print
The 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.  ... 
arXiv:1507.06524v1 fatcat:uqfcs3cmd5dz7imqqctvyiqry4

Burning a graph is hard

Stéphane Bessy, Anthony Bonato, Jeannette Janssen, Dieter Rautenbach, Elham Roshanbin
2017 Discrete Applied Mathematics  
The 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.  ... 
doi:10.1016/j.dam.2017.07.016 fatcat:n5hpmiwmd5dxlhcqozii2gmo4m

Burning graphs through farthest-first traversal [article]

Jesús García Díaz, Julio César Pérez Sansalvador, Lil María Xibai Rodríguez Henríquez, José Alejandro Cornejo Acosta
2021 arXiv   pre-print
The 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.  ... 
arXiv:2011.15019v4 fatcat:6ntrjvx6unhmfpdvlhbsuxpcoy

Approximation Algorithms for Graph Burning [article]

Anthony Bonato, Shahin Kamali
2019 arXiv   pre-print
Numerous approaches study the vulnerability 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  ... 
arXiv:1811.04449v2 fatcat:jcqhaua2rjdmplmjs67mywtfjy

APX-Hardness and Approximation for the k-Burning Number Problem [article]

Debajyoti Mondal, N. Parthiban, V. Kavitha, Indra Rajasingh
2021 arXiv   pre-print
The 1-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.  ... 
arXiv:2006.14733v2 fatcat:fiuxovnyzjh7dmvgyxbesxk3wm

The Burning Number of Directed Graphs: Bounds and Computational Complexity [article]

Remie Janssen
2020 arXiv   pre-print
The 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.  ... 
arXiv:2001.03381v1 fatcat:d7jq2mojcjcatdbwd6ypmmafzq

Bayesian Analysis of Social Influence [article]

Johan Koskinen, Galina Daraganova
2022 arXiv   pre-print
The basic influence 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  ... 
arXiv:2006.16464v3 fatcat:u6rgceft2rbajdx6bmzpejljzy

Spread and defend infection in graphs [article]

Arya Tanmay Gupta
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.  ... 
arXiv:2101.10814v3 fatcat:iekr36cyhbfjhfj6hv4l6su4uq

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

Anthony Bonato, Thomas Lidbetter
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] .  ... 
arXiv:1707.09968v1 fatcat:b2n2hmrnorbzteoyru4jcxjjpe

New heuristics for burning graphs [article]

Zahra Rezai Farokh, Maryam Tahmasbi, Zahra Haj Rajab Ali Tehrani and Yousof Buali
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.  ... 
arXiv:2003.09314v1 fatcat:jtt3aolpifhd7lcxaeux6krkuu

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

Shahin Kamali, Avery Miller, Kenny Zhang
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.  ... 
arXiv:1909.00530v2 fatcat:z36cpdfxongkfgh3kuziic4vwm

Improved Bounds for Burning Fence Graphs [article]

Anthony Bonato, Sean English, Bill Kay, Daniel Moghbel
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.  ... 
arXiv:1911.01342v1 fatcat:xtiewm4hcnhtvpgtriwlt3kt44

Burning a Graph is Hard [article]

Anthony Bonato, Jeannette Janssen, Elham Roshanbin
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] .  ... 
arXiv:1511.06774v1 fatcat:e44bd3s5vbejrmxxqovb3yxq4u
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