R: Average nearest neighbor degree

knn {igraph} | R Documentation

## 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)

[Package igraph version 1.2.10 Index]