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ba-networks.Rmd
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---
title: "ba-networks"
author: "Robert Jankowski"
date: "`r format(Sys.time(), '%d %B, %Y')`"
output:
pdf_document: default
html_document: default
---
```{r setup, include=FALSE}
library(tidyverse)
knitr::opts_chunk$set(echo = TRUE)
```
```{r}
load_file <- function(filename) {
df <- read.csv(filename, header = FALSE)
colnames(df) <- c("degree")
df
}
log_scale <- function(x, n) exp(seq(log(x[1]), log(x[length(x)]), length.out = n))
fit_powerlaw <- function(ba, bins = 20) {
log_breaks <- seq(min(ba$degree), max(ba$degree), length.out = bins)
log_breaks <- log_scale(log_breaks, bins)
h_degree <- hist(ba$degree, breaks = log_breaks, plot = FALSE)
degree_fit <- lm(log(h_degree$density)~log(h_degree$mids))
A <- degree_fit$coefficients[1]
alpha <- degree_fit$coefficients[2]
list(x = h_degree$mids,
y = h_degree$density,
log_breaks = log_breaks,
A = A,
alpha = alpha)
}
```
## Degree distribution
```{r}
library(zeallot)
min_max <- function(a1, a2, a3) {
a_min <- min(a1, a2, a3)
a_max <- max(a1, a2, a3)
c(a_min, a_max)
}
plot_by_m <- function(ba_m, colour) {
points(ba_m$x, ba_m$y, pch = 19, col = colour)
lines(ba_m$log_breaks, exp(ba_m$A) * ba_m$log_breaks ** ba_m$alpha,
col = colour, lty = 1, lwd = 2)
}
legend_description <- function(m, alpha) {
paste("m=", m, " | alpha= ", round(alpha, 2), sep = "")
}
plot_degree_distribution_m <- function(fit_ba_models, size) {
ba_m_1 <- fit_ba_models$ba_m_1
ba_m_2 <- fit_ba_models$ba_m_2
ba_m_5 <- fit_ba_models$ba_m_5
c(y_min, y_max) %<-% min_max(ba_m_1$y, ba_m_2$y, ba_m_5$y)
c(x_min, x_max) %<-% min_max(ba_m_1$x, ba_m_2$x, ba_m_5$x)
plot(ba_m_1$x, ba_m_1$y, log = "xy", pch = 19, xlab = "k", ylab = "P(k)",
col = "red", ylim = c(y_min, y_max), xlim = c(x_min, x_max),
main = paste("BA degree distribution N = ", size))
lines(ba_m_1$log_breaks, exp(ba_m_1$A) * ba_m_1$log_breaks ** ba_m_1$alpha,
col = "red", lty = 1, lwd = 2)
plot_by_m(ba_m_2, "blue")
plot_by_m(ba_m_5, "green")
m_1 <- legend_description(1, ba_m_1$alpha)
m_2 <- legend_description(2, ba_m_2$alpha)
m_5 <- legend_description(5, ba_m_5$alpha)
legend("topright", legend = c(m_1, m_2, m_5), col = c("red", "blue", "green"),
lty = 1, cex = 1)
}
```
```{r}
get_degree_and_fit <- function(filenames, bins) {
ba_m_1 <- load_file(filenames$m_1)
ba_m_2 <- load_file(filenames$m_2)
ba_m_5 <- load_file(filenames$m_5)
fit_ba_m_1 <- fit_powerlaw(ba_m_1, bins = bins)
fit_ba_m_2 <- fit_powerlaw(ba_m_2, bins = bins)
fit_ba_m_5 <- fit_powerlaw(ba_m_5, bins = bins)
list(ba_m_1 = fit_ba_m_1,
ba_m_2 = fit_ba_m_2,
ba_m_5 = fit_ba_m_5)
}
```
```{r}
# png("ba_n=100.png", width = 600, height = 400)
filenames_n_100 <- list(m_1 = "output/ba_degree_n=100_m=1.txt",
m_2 = "output/ba_degree_n=100_m=2.txt",
m_5 = "output/ba_degree_n=100_m=5.txt")
fit_ba_n_100 <- get_degree_and_fit(filenames_n_100, 7)
plot_degree_distribution_m(fit_ba_n_100, 100)
# dev.off()
```
```{r}
# png("ba_n=1000.png", width = 600, height = 400)
filenames_n_1000 <- list(m_1 = "output/ba_degree_n=1000_m=1.txt",
m_2 = "output/ba_degree_n=1000_m=2.txt",
m_5 = "output/ba_degree_n=1000_m=5.txt")
fit_ba_n_1000 <- get_degree_and_fit(filenames_n_1000, 10)
plot_degree_distribution_m(fit_ba_n_1000, 1000)
# dev.off()
```
```{r}
# png("ba_n=10000.png", width = 600, height = 400)
filenames_n_10000 <- list(m_1 = "output/ba_degree_n=10000_m=1.txt",
m_2 = "output/ba_degree_n=10000_m=2.txt",
m_5 = "output/ba_degree_n=10000_m=5.txt")
fit_ba_n_10000 <- get_degree_and_fit(filenames_n_10000, 10)
plot_degree_distribution_m(fit_ba_n_10000, 10000)
# dev.off()
```
```{r}
# png("ba_n=100000.png", width = 600, height = 400)
filenames_n_100000 <- list(m_1 = "output/ba_degree_n=100000_m=1.txt",
m_2 = "output/ba_degree_n=100000_m=2.txt",
m_5 = "output/ba_degree_n=100000_m=5.txt")
fit_ba_n_100000 <- get_degree_and_fit(filenames_n_100000, 15)
plot_degree_distribution_m(fit_ba_n_100000, 100000)
# dev.off()
```
```{r}
# png("ba_n=1000000.png", width = 600, height = 400)
filenames_n_1000000 <- list(m_1 = "output/ba_degree_n=1000000_m=1.txt",
m_2 = "output/ba_degree_n=1000000_m=2.txt",
m_5 = "output/ba_degree_n=1000000_m=5.txt")
fit_ba_n_1000000 <- get_degree_and_fit(filenames_n_1000000, 15)
plot_degree_distribution_m(fit_ba_n_1000000, 1000000)
# dev.off()
```
## Clustering coefficient
```{r, warning=FALSE, message=FALSE}
library(ggthemes)
clustering_avg_length <-
read.csv("output/ba_simulation_par_new_clustering.txt", header = FALSE, col.names = c("C", "N")) %>%
left_join(read.csv("output/ba_simulation_par_new_avg_path.txt", header = FALSE, col.names = c("l", "N"))) %>%
mutate(l_theory = log(N) / log(log(N)))
ggplot(clustering_avg_length) +
geom_line(aes(N, l_theory / 3, color = "ln(N) / ln(ln(N))"), size = 1.1) +
geom_point(aes(N, C, color = "clustering coefficient"), size = 2.5) +
geom_point(aes(N, l / 3, color = "average path length"), size = 2.5) +
scale_y_continuous("C", sec.axis = sec_axis(~ .*3, name = "l")) +
scale_x_log10() +
theme_few() +
labs(color = "") +
theme(legend.position = "top", panel.grid.minor = element_line(size = 0.2, colour = "grey"))
# ggsave("ba_clustering_average_path.png")
```