igraph (version 0.6-2)

graph.knn: Average nearest neighbor degree

Description

Calculate the average nearest neighbor degree of the given vertices and the same quantity in the function of vertex degree

Usage

graph.knn(graph, vids=V(graph), weights=NULL)

Arguments

graph

The input graph. It can be directed, but it will be treated as undirected, i.e. the direction of the edges is ignored.

vids

The vertices for which the calculation is performed. Normally it includes all vertices. Note, that if not all vertices are given here, then both knn and knnk will be calculated based

weights

Weight vector. If the graph has a weight edge attribute, then this is used by default. If this argument is given, then vertex strength (see graph.strength) is used instead of

Value

• A list with two members:
• knn
  A numeric vector giving the average nearest neighbor degree for all vertices in vids.
• knnk
  A numeric vector, its length is the maximum (total) vertex degree in the graph. The first element is the average nearest neighbor degree of vertices with degree one, etc.

Details

Note that for zero degree vertices the answer in knn is NaN (zero divided by zero), the same is true for knnk if a given degree never appears in the network.

References

Alain Barrat, Marc Barthelemy, Romualdo Pastor-Satorras, Alessandro Vespignani: The architecture of complex weighted networks, Proc. Natl. Acad. Sci. USA 101, 3747 (2004)

Examples

# Some trivial ones
g <- graph.ring(10)
graph.knn(g)
g2 <- graph.star(10)
graph.knn(g2)

# A scale-free one, try to plot 'knnk'
g3 <- ba.game(1000, m=5)
graph.knn(g3)

# A random graph
g4 <- random.graph.game(1000, p=5/1000)
graph.knn(g4)

# A weighted graph
g5 <- graph.star(10)
E(g5)$weight <- seq(ecount(g5))
graph.knn(g5)