WK9Challenge_KDocekal

Code

library(tidyverse)
library(igraph)
library(statnet)
library(gssr)
library(drat)

knitr::opts_chunk$set(echo = TRUE)

My dataset uses results from the 1985 General Social Survey. The data frame is based on “talkto,” which provides weighted edges based on members a respondent’s group of contacts. Weights are based on respondents’ perception of how much each contact talks to each other.

Code

remotes::install_github("kjhealy/gssr")

Skipping install of 'gssr' from a github remote, the SHA1 (abe949b1) has not changed since last install.
  Use `force = TRUE` to force installation

Code

drat::addRepo("kjhealy")

gss85 <- gss_get_yr(1985)

Fetching: https://gss.norc.org/documents/stata/1985_stata.zip

Code

ties <- gss85[,grepl("talkto", colnames(gss85))]

mat = matrix(nrow = 5, ncol = 5)

mat[lower.tri(mat)] <- as.numeric(ties[3,])

mat[upper.tri(mat)] = t(mat)[upper.tri(mat)]

na_vals <- is.na(mat)
non_missing_rows <- rowSums(na_vals) < nrow(mat)
mat <- mat[non_missing_rows,non_missing_rows]

diag(mat) <- 0


ig.net <- graph.adjacency(mat, mode = "undirected", weighted = T)

Results show that there is 1 component and the median weight is 2.This network contains 5 vertices and 10 edges. Ties are not bipartite or directed but they are weighted.

Code

igraph::components(ig.net)$no

[1] 1

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summary(E(ig.net)$weight)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
    1.0     2.0     2.0     1.8     2.0     2.0 

Code

vcount(ig.net)

[1] 5

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ecount(ig.net)

[1] 10

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is_bipartite(ig.net)

[1] FALSE

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is_directed(ig.net)

[1] FALSE

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is_weighted(ig.net)

[1] TRUE

In the following tests I compare our networks network degree centralization, betweeness centrality, and transitivity with random networks to establish potential significance. These test let us determine if our sampled ego network is representative of the population in terms of important indicators of network characteristics. Doing so will help us establish the significance of any further tests such as on tie strength. Such tests will enable us to shed light on the attitudes of the network’s nodes as interpersonal attitudes are strong influences of unit formation (Heider, F. (1946). Attitudes and cognitive organization.).

To test our null hypothesis that our network’s transitivity is higher or lower than expected compared to a random network we can use a CUG-test. First we test transitivity conditioned on network size. Results show that we should accept the alternative hypothesis that the observed transitivity is higher than expected compared to a random network.

Code

trans.cug<-cug.test(mat,FUN=gtrans,mode="digraph",cmode="size")
trans.cug

Univariate Conditional Uniform Graph Test

Conditioning Method: size 
Graph Type: digraph 
Diagonal Used: FALSE 
Replications: 1000 

Observed Value: 1 
Pr(X>=Obs): 0.005 
Pr(X<=Obs): 1 

Code

plot(trans.cug)

Code

cug.t(trans.cug)

Error in cug.t(trans.cug): could not find function "cug.t"

If we instead test transitivity conditioned on dyads we get similar results and reject the null hypothesis.

Code

trans.cug<-cug.test(mat,FUN=gtrans,mode="digraph",cmode="dyad")
trans.cug

Univariate Conditional Uniform Graph Test

Conditioning Method: dyad.census 
Graph Type: digraph 
Diagonal Used: FALSE 
Replications: 1000 

Observed Value: 1 
Pr(X>=Obs): 1 
Pr(X<=Obs): 1 

Code

plot(trans.cug)

Code

cug.t(trans.cug)

Error in cug.t(trans.cug): could not find function "cug.t"

Alternatively, test transitivity can also be conditioned on edges which results in a similar outcome.

Code

trans.cug<-cug.test(mat,FUN=gtrans,mode="digraph",cmode="edges", reps=100)
trans.cug

Univariate Conditional Uniform Graph Test

Conditioning Method: edges 
Graph Type: digraph 
Diagonal Used: FALSE 
Replications: 100 

Observed Value: 1 
Pr(X>=Obs): 1 
Pr(X<=Obs): 1 

Code

plot(trans.cug)

Code

cug.t(trans.cug)

Error in cug.t(trans.cug): could not find function "cug.t"

We can also test network degree centralization to the null conditional based on size. In this case, results indicate that we cannot reject the null hypothesis for network degree centralization. The t-statistic results show a score of -.62.

Code

c.degree.cug <-cug.test(mat,FUN=centralization,  FUN.arg=list(FUN=degree, cmode="indegree"), mode="digraph", cmode="size") 

plot(c.degree.cug)

Code

cug.t(c.degree.cug)

Error in cug.t(c.degree.cug): could not find function "cug.t"

Here we test betweeness centrality with 100 reps. Results show that we should accept the alternative hypothesis that the observed betweeness centrality is lower than expected compared to a random network.

Code

b.degree.cug <-cug.test(mat,FUN=centralization,  FUN.arg=list(FUN=betweenness, cmode="directed"), mode="digraph", cmode="size", reps=100) 

plot(b.degree.cug)

Code

cug.t(b.degree.cug)

Error in cug.t(b.degree.cug): could not find function "cug.t"