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

## Usage

sample_forestfire(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.

## Value

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

## 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.

## 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.

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.