# traits

0th

Percentile

##### Graph generation based on different vertex types

These functions implement evolving network models based on different vertex types.

Keywords
graphs
##### Usage
callaway.traits.game (nodes, types, edge.per.step = 1, type.dist = rep(1,
types), pref.matrix = matrix(1, types, types), directed = FALSE)
establishment.game(nodes, types, k = 1, type.dist = rep(1, types),
pref.matrix = matrix(1, types, types), directed = FALSE)
##### Arguments
nodes
The number of vertices in the graph.
types
The number of different vertex types.
edge.per.step
The number of edges to add to the graph per time step.
type.dist
The distribution of the vertex types. This is assumed to be stationary in time.
pref.matrix
A matrix giving the preferences of the given vertex types. These should be probabilities, ie. numbers between zero and one.
directed
Logical constant, whether to generate directed graphs.
k
The number of trials per time step, see details below.
##### Details

For callaway.traits.game the simulation goes like this: in each discrete time step a new vertex is added to the graph. The type of this vertex is generated based on type.dist. Then two vertices are selected uniformly randomly from the graph. The probability that they will be connected depends on the types of these vertices and is taken from pref.matrix. Then another two vertices are selected and this is repeated edges.per.step times in each time step.

For establishment.game the simulation goes like this: a single vertex is added at each time step. This new vertex tries to connect to k vertices in the graph. The probability that such a connection is realized depends on the types of the vertices involved and is taken from pref.matrix.

##### Value

• A new graph object.

##### Aliases
• callaway.traits.game
• establishment.game
##### Examples
# two types of vertices, they like only themselves
g1 <- callaway.traits.game(1000, 2, pref.matrix=matrix( c(1,0,0,1), nc=2))
g2 <- establishment.game(1000, 2, k=2, pref.matrix=matrix( c(1,0,0,1), nc=2))
Documentation reproduced from package igraph, version 0.5.5-3, License: GPL (>= 2)

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