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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.  ...

### 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.  ...

### 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.  ...

### 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.  ...

### 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  M. Šimon, L. Huraj, I.  ...

### 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  ...

### 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.  ...

### 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.  ...

### 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  ...

### 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  and wburning  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]

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] .  ...

### 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 .  ...  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]

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.  ...

### 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.  ...

### 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  .  ...
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