# nSmooth: estimates probabilty matrix by neighborhood smoothing In randnet: Random Network Model Estimation, Selection and Parameter Tuning

 nSmooth R Documentation

## estimates probabilty matrix by neighborhood smoothing

### Description

estimates probabilty matrix by neighborhood smoothing of Zhang et. al. (2017)

### Usage

``````nSmooth(A, h = NULL)
``````

### Arguments

 `A` adjacency matrix `h` quantile value used for smoothing. Recommended to be in the scale of sqrt(log(n)/n) where n is the size of the network. The default value is sqrt(log(n)/n) from the paper.

### Details

The method assumes a graphon model where the underlying graphon function is piecewise Lipchitz. However, it may be slow for moderately large networks, though it is one of the fastest methods for graphon models.

### Value

the probability matrix

### Author(s)

Tianxi Li, Elizaveta Levina, Ji Zhu

Maintainer: Tianxi Li <tianxili@virginia.edu>

### References

Zhang, Y.; Levina, E. & Zhu, J. Estimating network edge probabilities by neighbourhood smoothing Biometrika, Oxford University Press, 2017, 104, 771-783

### Examples

``````

N <- 100

U = matrix(1:N,nrow=1) / (N+1)
V = matrix(1:N,nrow=1) / (N+1)

W = (t(U))^2
W = W/3*cos(1/(W + 1e-7)) + 0.15

upper.index <- which(upper.tri(W))

A <- matrix(0,N,N)

rand.ind <- runif(length(upper.index))

edge.index <- upper.index[rand.ind < W[upper.index]]

A[edge.index] <- 1

A <- A + t(A)
diag(A) <- 0

What <- nSmooth(A)

``````

randnet documentation built on May 31, 2023, 6:44 p.m.