---
title: "Exploring Community Structure"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{explore-comm}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
options(rmarkdown.html_vignette.check_title = FALSE)
```

```{r setup}
library(nett)
library(Matrix)
```

Let us create a simple degree-corrected planted parition (DCPP) model:
```{r}
set.seed(1)
n = 1000 # the number of nodes
Ktru = 4 # the number of true communties
lambda = 15 # the average degree
oir = 0.1 # the out-in ratio
pri = rep(1,Ktru)/Ktru
theta <- EnvStats::rpareto(n, 2/3, 3) # node conn. propensity parameter

B = pp_conn(n, oir, lambda, pri, theta)$B  # create connectivity matrix
z =  sample(Ktru, n, replace=T, prob=pri)  # sample node labels
A = sample_dcsbm(z, B, theta) # sample the adjacency matrix
```
Check to see if the average degree matches the target:
```{r}
mean(rowSums(A))
```
Compute and plot the community profile based on SNAC+ test statistic:
```{r}
tstat = snac_resample(A, nrep = 10, ncores = 1)
plot_smooth_profile(tstat, "A DCPP network")
```

See the article [Adjusted chi-square test for degree-corrected block models, Zhang and Amini](https://arxiv.org/abs/2012.15047) for how these profiles are constructed.