forest.fire.game {igraph} R Documentation

## Forest Fire Network Model

### Description

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

### 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:

1. 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.
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.

### Author(s)

Gabor Csardi csardi@rmki.kfki.hu

### 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.

### 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)
}
```

[Package igraph version 0.5 Index]