ECS 132 SS2022 HW3.pdf - ECS 132 Homework 3 Problem A:...

ECS 132 Homework 3
Problem A:
Download the DNC e-mail co-recipient dataset from canvas. Here we
will explore the degree distribution of the resulting graph.
● The format seems to be
recip1ID recip2ID nummsgs
● One might treat this as a weighted graph, but we will not do
so. Ignore the third column.
● The data seems to be duplicated, with (a,b) and (b,a) both
appearing in the data. This is odd, as the third column
differs, lets take only the rows in which recip1ID < recip2ID.
This indeed cuts the data in half.
● Explore how well a power law fits the data, as follows. Let m
i
denote the count of recipients having degree i in the data, i =
1,2,3,... The form of the pmf (check this!) implies that a plot
of log(m
i
) against log(i) should look like a straight line.
There will be points above and below the line, due to sampling
variation, but the trend should look linear. Make this plot,
and comment.
● NOTE: In this and all future work for the course, you must use R
to generate your graphs. This can be either base R, ggplot2
(appendix in our book) or lattice .
● Assuming a power law, estimate γ. (We use the term estimate here
because the data is only a sample from a population (real or
conceptual). Use R's lm() function for this. We will study this
function in detail later, but for instance the following would
find the intercept and slope of a line fit through the points
(1,1), (2,2), (3,4):
> x <- 1:3
> y <- c(1,2,4)
> lm(y ~ x)

●