# Homework 4 for the University of Tulsa' s CS-7863 Network Theory Course
# Degree Distribution
# Professor: Dr. McKinney, Spring 2022
# Noah Schrick - 1492657

library(igraph)
library(igraphdata)
data(yeast)
g <- yeast
g.netname <- "Yeast"

################# Set up Work #################
g.vec <- degree(g)
g.hist <- hist(g.vec, freq=FALSE, main=paste("Histogram of the", g.netname,
                                                 " Network"))
legend("topright", c("Guess", "Poisson", "Least-Squares Fit",
                "Max Log-Likelihood"), lty=c(1,2,3,4), col=c("#40B0A6", 
                                          "#006CD1", "#E66100", "#D35FB7"))

g.mean <- mean(g.vec)
g.seq <- 0:max(g.vec) # x-axis

################# Guessing Alpha #################
alpha.guess <- 1.5
lines(g.seq, g.seq^(-alpha.guess), col="#40B0A6", lty=1, lwd=3)

################# Poisson #################
g.pois <- dpois(g.seq, g.mean, log=F)
lines(g.seq, g.pois, col="#006CD1", lty=2, lwd=3)

################# Linear model: Least-Squares Fit #################
g.breaks <- g.hist$breaks[-c(1)] # remove 0
g.probs <- g.hist$density[-1] # make lengths match

# Need to clean up probabilities that are 0
nz.probs.mask <- g.probs!=0
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.probs[nz.probs.mask]

#plot(log(g.breaks.clean), log(g.probs.clean))
g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
summary(g.fit)
alpha.LM <- coef(g.fit)[2]
lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3, lwd=3)


################# Max-Log-Likelihood #################
n <- length(g.breaks.clean)
kmin <- g.breaks.clean[1]

alpha.ML <- 1 + n/sum(log(g.breaks.clean/kmin))
alpha.ML
lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4, lwd=3)