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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

knn(
  graph,
  vids = V(graph),
  mode = c("all", "out", "in", "total"),
  neighbor.degree.mode = c("all", "out", "in", "total"),
  weights = NULL
)

Arguments

`graph`	The input graph. It may be directed.
`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 on the given vertices only.
`mode`	Character constant to indicate the type of neighbors to consider in directed graphs. `out` considers out-neighbors, `in` considers in-neighbors and `all` ignores edge directions.
`neighbor.degree.mode`	The type of degree to average in directed graphs. `out` averages out-degrees, `in` averages in-degrees and `all` ignores edge directions for the degree calculation.
`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 `strength`) is used instead of vertex degree. But note that `knnk` is still given in the function of the normal vertex degree. Weights are are used to calculate a weighted degree (also called `strength`) instead of the degree.

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.

The weighted version computes a weighted average of the neighbor degrees as

k_nn_u = 1/s_u sum_v w_uv k_v,

where s_u = sum_v w_uv is the sum of the incident edge weights of vertex u, i.e. its strength. The sum runs over the neighbors v of vertex u as indicated by mode. w_uv denotes the weighted adjacency matrix and k_v is the neighbors' degree, specified by neighbor_degree_mode.

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.

Author(s)

Gabor Csardi csardi.gabor@gmail.com

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 <- make_ring(10)
knn(g)
g2 <- make_star(10)
knn(g2)

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

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

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

igraph

Network Analysis and Visualization

v1.2.10

GPL (>= 2)

Authors

See AUTHORS file.

Initial release

knn