# forest.fire.game

0th

Percentile

##### Forest Fire Network Model

This is a growing network model, which resembles of how the forest fire spreads by igniting trees close by.

Keywords
graphs
##### Usage
forest.fire.game (nodes, fw.prob, bw.factor = 1, ambs = 1, directed = TRUE)
##### Arguments
nodes
The number of vertices in the graph.
fw.prob
The forward burning probability, see details below.
bw.factor
The backward burning ratio. The backward burning probability is calculated as bw.factor*fw.prob.
ambs
directed
Logical scalar, whether to create a directed graph.
##### Details

The forest fire model intends to reproduce the following network characteristics, observed in real networks:

• Heavy-tailed in-degree distribution.
• Heavy-tailed out-degree distribution.
• Communities.
• Densification power-law. The network is densifying in time, according to a power-law rule.
• Shrinking diameter. The diameter of the network decreases in time.

The network is generated in the following way. One vertex is added at a time. This vertex connects to (cites) ambs vertices already present in the network, chosen uniformly random. Now, for each cited vertex $v$ we do the following procedure:

1. We generate two random number,$x$and$y$, that are geometrically distributed with means$p/(1-p)$and$rp(1-rp)$. ($p$isfw.prob,$r$isbw.factor.) The new vertex cites$x$outgoing neighbors and$y$incoming neighbors of$v$, from those which are not yet cited by the new vertex. If there are less than$x$or$y$such vertices available then we cite all of them.
2. The same procedure is applied to all the newly cited vertices.

##### Value

• A simple graph, possibly directed if the directed argument is TRUE.

##### Note

The version of the model in the published paper is incorrect in the sense that it cannot generate the kind of graphs the authors claim. A corrected version is available from http://www.cs.cmu.edu/~jure/pubs/powergrowth-tkdd.pdf, our implementation is based on this.

##### concept

• Random graph model
• Forest fire model

##### References

Jure Leskovec, Jon Kleinberg and Christos Faloutsos. Graphs over time: densification laws, shrinking diameters and possible explanations. KDD '05: Proceeding of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining, 177--187, 2005.

barabasi.game for the basic preferential attachment model.

##### Aliases
• forest.fire.game
##### Examples
g <- forest.fire.game(10000, fw.prob=0.37, bw.factor=0.32/0.37)
dd1 <- degree.distribution(g, mode="in")
dd2 <- degree.distribution(g, mode="out")
if (interactive()) {
plot(seq(along=dd1)-1, dd1, log="xy")
points(seq(along=dd2)-1, dd2, col=2, pch=2)
}
Documentation reproduced from package igraph, version 0.6.5-2, License: GPL (>= 2)

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