knn: Average nearest neighbor degree

In igraph: Network Analysis and Visualization

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} = \frac{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.

Related documentation in the C library

igraph_avg_nearest_neighbor_degree().

Author(s)

Gabor Csardi [e-mail]

References

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

See Also

Other structural.properties: bfs(), component_distribution(), connect(), constraint(), coreness(), degree(), dfs(), distance_table(), edge_density(), feedback_arc_set(), girth(), is_acyclic(), is_dag(), is_matching(), k_shortest_paths(), reciprocity(), subcomponent(), subgraph(), topo_sort(), transitivity(), unfold_tree(), which_multiple(), which_mutual()

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 documentation built on Oct. 20, 2024, 1:06 a.m.