# forest.fire.game

##### 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,
verbose = igraph.par("verbose"))
```

##### 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
- The number of ambassador vertices.
- directed
- Logical scalar, whether to create a directed graph.
- verbose
- Logical scalar, whether to
draw a progress bar.

##### 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:

- We generate two random number,$x$and$y$, that are
geometrically distributed with means$p/(1-p)$and$rp(1-rp)$. ($p$is
`fw.prob`

,$r$is`bw.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. - 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

##### 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.

##### See Also

`barabasi.game`

for the basic preferential attachment
model.

##### 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 0.5.3, License: GPL (>= 2)*